This is a lovely answer. OP, try to understand where your parents are coming from and grin and bear it 
You’ll find your people and a big state school is probably a great place to do that.
FWIW, I wouldn’t pay for Oberlin I also wouldn’t pay for Liberty. So I guess I get your parents a little bit!
I read this, and the fact that you’re from LA, and the University of Rochester also popped up as a place you should consider (super easy to double major, excellent for music and STEM with tons of research - a research culture dominates the school). Merit aid isn’t a sure thing, but I really expect you’d be competitive for it. If you look at the school and like it, it’s worth a shot. It’s only 15 minutes from the Rochester (NY) airport.
I also think you might want to consider the University of Miami (FL). I’ve seen really good merit awards from there too, but I’m not sure they’re as much of what you are looking for. It’s is in an “approved” state.
I bet you’d be competitive for large(r) awards at Pitt and Case Western too. Pitt is rolling admissions, so you would know quickly about that part. The highest merit awards are announced later.
I’m actually thinking Washington & Lee - the Johnson goes to 10% of incoming and they have other scholarships that are tuition only - so you might be a fine candidate.
There’s “not great” skiing not far - it’s heavily greek but not that kind of greek - and it’s academically stellar. it’s a small LAC.
It’s not a primary for you but it’s a target for admission and a reach for the Johnson - but if 40+ are getting it, why not you?
If you’re from New Orleans (are you?) and don’t get the Washington, there’s a full tuition one.
No, I’m from Northern LA
There’s still the Johnson.
And smaller schools like Truman State or UAH that could work (sams skiing). Or Hendrix or Ogelthorpe for affordable LACs as they’ll match LSU.
Don’t make the mistake of thinking certain schools are only Greek.
My son is at Alabama, is not Greek, doesn’t care about football although he’s been to a few games.
The Honors Dorm (Ridgecrest) was ‘boring’ and they have Randall Research Scholars and Blount Scholars.
I’m sure other SEC schools you might assume are party/Greek are similar - tons of smart kids who don’t party and don’t love sports. They likely have extra programs above Honors for the best and brightest. And they will be inexpensive.
Bama the cheapest but Auburn, UF, UGA, Mizzou, Ms State…many of them.
Some kids will be liberal. Some wont be. And most that don’t ever think in that lens or care about it.
Good luck
Based on some of your preferences, these previously-mentioned full-ride National Merit schools might interest you:
UT-Dallas. Dallas is a fun city with lots of culture and arts. The school is not a party school, but rather is known for nerdy fun. It is a STEM-focused school, but also has humanities majors and minors including a Visual and Performing Arts major that has various tracks including a music track. Super LGBT friendly. One of my S22’s good friends is a NMS, and she is really loving it so far. You get your own room in the dorm! Dallas is easy to get to because it is an airport hub.
UCF-Big school but the honors college makes it feel smaller. Pretty much any major you could want including a great aerospace engineering dept. Super LGBT progressive. Happy students.
University of Tulsa-This school’s president is making a big push to recruit lots of National Merit Scholars, so you would have lots of peers. Has both STEM and music. As Blossom says above, Tulsa is “young, hip, urban and cool.”
University of Maine- Far away from you but near nature and skiing. It seems to be an up and coming school, there has been more buzz about it lately. Has the benefits of being a flagship (lots of majors) but smaller size ~10,000. Engineering department seems friendly and down to earth.
For once W&L’s conservative reputation will be a selling point!
(However, OP, it is absolutely welcoming to all and has left leaning kids and faculty (eg both voted to drop “Lee” from the school name)).
Thanks!
Yeah I actually know a girl that got a full ride there. Or a big scholarship, I’m not sure which.
Their big scholarship is a full ride plus a $7,000 stipend.
Oh wow. So they pay you to go there?
A couple thoughts…
First, except for a couple outliers like BYU or Liberty U almost every university in the US would be considered “liberal” compared to northern LA. Even schools in supposedly “conservative” states like TX lean left - think UT Austin. That said, some schools in the US are famous, or infamous, for their leftward bent (UW Madison, UC Berkeley, Vasser, Brown, etc.).
Second, you need to distinguish between schools where the faculty and students are generally liberal politically (in the US generally defined as supporting larger government, higher taxes, greater regulation, a large welfare state, more open on social issues, etc.), and schools where the regressive left runs the show. By regressive left, I refer to activists - both students and faculty - who silence opposing views through speech codes, uninviting or shouting down speakers, ostracizing or even marking down students who voice conservative, or even moderate, viewpoints, etc. One of the most egregious examples of the regressive left being in charge is Evergreen State (if you are not familiar, search for Bret Weinstein).
There are many schools in the US that lean left, where you will be comfortable, but have not been taken over by the regressive left. I would concentrate on these. You can learn more about them on websites like FIRE and Heterodox Academy. My guess is that most highly ranked schools in the south would fit the bill, like Duke, UNC, and UVA from earlier posts. Focus on schools where all backgrounds and viewpoints are welcome and you will have a richer college experience.
I think a bigger question for your parents, regardless of where you go to school, is your intended major. You wanted to be open with interests in music, bio and STEM. That means a university that offers disparate programs and rules out many small LACs. Note that you will need to apply to the most competitive program in which your are interested. Students can switch from engineering to bio or history, but not the other way. My guess is your parents would balk if you chose women’s studies.
Perfect - so he is the ultimate proof that someone raised with good values and principles (like you have been), can be trusted to stand by those, regardless of how people around him might feel/act!
They should agree with you, that quite evidently you are an exceptional student, because you have good work ethics, and maintained that despite your parental situation (caused by them) - regardless of what temptations and peer pressure you might have encountered as a teenager.
You have proven that you can be trusted to make good choices they can be proud of, and will continue to do so, now that you’re an adult!
Let’s take some “iconic” people:
Tucker Carlson was educated in San Diego, Rhode Island and went to Trinity College (an (unaffiliated liberal arts college) in Hartford, CT. Any indoctrination clearly went sideways?
Donald Trump attended College in NYC, later transferred to UPenn.
Kellyanne Conway attended Trinity College in DC - where the Arts & Sciences College is a women’s college. Famously has husband & child!
Rudy Giuliani attended Manhattan College, a liberal arts college, and attended NYU 
for his law degree.
While some people might argue that they are not poster-children for having learned “critical thinking”, it hopefully does make the point that being educated in the “liberal states”, at “liberal art colleges” does not result in brainwashing or get one infected by the queer virus.
Sometimes the same word is used to describe completely different concepts. Getting a “shot” at my Doctor isn’t the same as getting one at a bar, or… worse.
The “liberales artes” is a term going back to the ancient Greek, thousands of years before the term was used to label political thinking. Those “artes” simply were the teachings suitable for a free person, allowing for inquisitive examination of the world around us, rather than learning that is restricted.
Today, it’s the overarching term for the studies in the natural sciences, social sciences, arts and humanities - such as biology, physics, computer science, economics, psychology, music.
So, whenever your Dad turns on his tablet to schedule an appointment with his doctor, or to listen to his favorite classic album, and uses the monetary system to pay with dollars… he should be thanking the “liberal” sciences many-times over. 
You might want to look at Case Western. They are strong in engineering, the life sciences (#12 in BioMed) and the performing arts. They encourage double majors and minors, and students are not locked into their major until late sophomore year. They are also generous with merit aid. I do not know if they offer a full National Merit scholarship.
I mean that if Alabama or Dallas or Arizona is a full ride, and Utah is 25K/yr, the 25K/yr that you wouldn’t have to spend at the full-ride school leaves a LOT of money for going to SLC or anywhere else to ski. For the 25K/yr that you’d have to pay at Utah, but wouldn’t have to pay at the full ride school, could buy you a lot of skiing, traveling, whatever.
I attended the University of Wisconsin having grown up in a right-leaning home, and I managed to make my way through it without morphing into Stalin. And I did take some Sociology, Poli Sci, Psych, Criminology, and History courses. The students were mostly leaning left, but not rabidly so, and there was a healthy College Republicans group. (I didn’t join it; I joined a fraternity with my two closest frosh dorm pals)
College should teach you how to think, not what to think. And In none of the classes I took did one of the professors try to shove what I recognized as leftist propaganda down our throats. In Criminology the prevailing thought was that poverty leads to crime. Well, duh, sometimes it can. But – what leads to poverty? The professor did not delve down that particular rabbit hole.
I know that students exist who try to shout others down, but I have to believe that even at the most reputably liberal places – like Wesleyan, Vassar, Bard, Hampshire (?) – they are the exception proving the rule of a general sense of welcoming and respect.
If that helps relax your folks a bit – a fiscal conservative/social moderate Christian making it through UW without a Che t-shirt – feel free to let them know.
You can go almost anywhere and find your people. Or, make friends of another stripe – many people can debate in a respectful manner and still be our friends. That’s how we keep the world spinning.
I attended CMU in the 80s and the school was an odd mix of conservative engineering and more liberal fine arts students (one college guide at the time described it as “fruits and nuts”). Unlike you, I did have a liberal - actually a hard core leftist - professor who did push his world view in a class on South American Political Economies, or some such thing. He spent time with the Sandinistas in El Salvador and he waxed poetic about how wonderful they were, how Communism was the way to go, and how Reagan was the devil. He nearly blew a gasket when ROTC students asked about left wing death squads and whether he thought it was odd that the Sandinistas never let him go anywhere unaccompanied. It never dawned on him that he was the useful idiot.
“Dad/Mom, that’s where the best internships are”.
Then, if they try to push you into a political conversation, avoid it by saying, “Nothing is going to change what you’ve taught me, I just want to make sure that I’m going to have a job after I graduate.”
Gordon College in Wenham MA would satisfy parents and has a good music program.
OP you don’t even have to minor in music to continue lessons and do extracurricular performance at many schools.
Folks have suggested U of Rochester and mentioned strength in music but I want to caution you that yes Eastman at U or Rochester is excellent but you would not be in that degree program. If you look at schools that do have a BM program, check to see if the best teachers and opportunities go to those students.
A liberal arts school may be your best bet as long as you parents understand the word “liberal” in that context.
I sent you the link. The Johnson Scholarship. See my previous note.