For the “prestige private” colleges, the ones that use only your custodial parent household are Chicago and Vanderbilt. If your custodial parent is remarried, Princeton also qualifies. You may want to go to each their financial aid web sites and run the net price calculator to see if need-based financial aid there will be realistic.
The other “prestige private” colleges generally require both parents’ finances, so any net price calculator use must include both of their finances.
From what you describe, it’s extremely unlikely that you would qualify for any financial aid. I do not know of any scenario where a college would take into account that you have younger siblings who are not in college when considering your need for financial aid. And you are correct, your parents do have other substantial financial obligations, what with there being a number of younger children at each household, each of whom will need a college education. They might not all be National Merit Finalists, either, with the scholarship opportunities that come along with that.
If you get NMF and find a college that you like that gives a full ride for NMF (or get some other merit full ride at some college), then you would become much less dependent financially on your parents, if you are concerned about them changing their mind about funding your college after you start.
If your parents are worried let them know
many colleges have Christian fellowships (other religious groups too) and communities that are very strong and prominent on college campuses where students are involved like Cru (formerly CCC) FCA, Young Life, Navigators that you can even find at JHU, UVA, UMD, VA tech, Dartmouth, northwestern, Rice, etc. you can investigate and look at the different organizations. Not vanderbilt - they have a policy that is somewhat against religious groups on campus but the Nashville overall is conservative. At least at some of these schools have balance of liberalism and conservatism. Not sure what your parents are looking for when they say “conservative” but maybe this type of argument could persuade them to let you go wherever you want.
OP:
If you end up getting NMF, then that makes Univ of Arizona in play with its National Merit scholarships. U of A is in Tucson. Tucson is much more liberal than the rest of the state (Tucson-area Congressional representatives, for example, always end up blue instead of red). Tucson also has a pretty decent LGBT+ scene. There’s also plenty of red-purple students who attend U of A. And it’s large enough that you can find your proverbial tribe…that logic would apply to any larger university, of course.
What sorts of things are you interested in studying in college?
I want to be able to study a lot of different things and not be bound just to my major. I think I I ant to major in bio with either a music double major or minor (I’ll start with a minor in music and add the major if I think my gpa, schedule, and mental health can handle it) so both of those. I might do biomedical or aerospace engineering instead. I don’t know but I have some time to decide. Definitely STEM though. I don’t want a super big party scene (LSU, Alabama, etc) but I also don’t want somewhere that’s all academics and no fun. I might join a sorority if the Greek scene is chill but not at a big SEC school or similar environment. I love the mountains (or other pretty outdoor things—where I live is just trees and a few small hills) and hiking. I’d like the vibe to be open and accepting, and it would be great if there is a big arts scene but I can find that crowd anywhere. Sports would be fun to attend, but I don’t play any and it’s not a necessity. Good merit aid is a must. I’d like it to be somewhere where it’s pretty easy to double major, even if I don’t end up being able to do it. Being able to ski would be amazing, but that’s just a random little thing that isn’t important. I’d like to be either in a medium to large city or somewhere with a cool campus or college town. Not like a super boring place. Also I would rather go somewhere that’s bigger than 2,000 people, but if it’s over 25,000 I’d want to be able to be in an honors college type thing. I toured university of Arkansas and I liked it except that it seemed terrifyingly huge. But none of these things are requirements, just things that would be nice to have.
this is extremely accurate and a great post - also in general, more educated people on college campuses are more accepting of others opinions.
Many of the state schools down south your parents would approve of actually incentivize kids from the mid atlantic and northeast to attend and tend to make those campuses more “liberal” those kids often head south just for the weather/ college footbal etc…
U of Utah. Excellent STEM, excellent music, best in the world skiing very close to school, plus fantastic hiking literally right next to campus, plus much more.
Salt Lake is developing an exciting, Portandesque kind of young urban scene. Your parents will think it is Conservative with a Capital C, but it’s actually quite liberal! Good LGBTQ scene, too. Beautiful campus in the foothills of the city, walking, biking, light rail downhill to the core of the city, with bars, restaurants, culture, etc.
They’ll probably give you a full tuition scholarship, don’t know if you could get a full ride.
The University of Utah would fulfill a lot of your wish list. And might be somewhat reassuring to your parents, even though SLC is more liberal than the state as a whole. Merit aid is pretty good for 4.0 students, albeit not at the level of places like Alabama.
Edit: I see @parentologist has the same idea
App State?
I would tell my parents that they should have faith in their parenting skills and that they helped mold me into a respectful human being. That by allowing me to go to college helps me bring more goodness into the world.
Admittedly, I would be snarky with my parents and add something like “are you worried you didn’t raise me right?” But for you, that will NOT fly! 
It’s not really mormon? Not that there’s anything wrong with that but I’ve heard they’re generally with southern baptists in their beliefs and it’s Utah
No, the U isn’t that Mormon. In fact, SLC isn’t that Mormon. The Mormon kids go to BYU Provo. Some do go the U of course, but it’s not a Mormon school, far from it.
Or asking how my stepbrothers super religious school that brings religion into all their classes including history and science (science of all things?) isn’t indoctrination but lots of secular colleges are…but that wouldn’t be helpful.
Now, now. You want them to pay for college? Keep your mouth shut and your snarky opinions to yourself.
U of Utah max out of state annual merit is 25K/yr, still leaving you with 25K/yr to pay. If it were me, I’d take the full ride and ask your parents to foot a ski vacation, for a lot less than 25K/yr!
I was also going to suggest University of Utah!
Plus after the first year you will qualify for in-state tuition if you meet certain requirements about remaining in the state for specific periods of time during your education which might be a good financial benefit as well.
I know! I wouldn’t say that to them. That would be really rude. I was responding to another person’s similar comment
What do you mean by the ski trip?
I was a first gen college student born to nonreligious blue collar parents that are still right leaning. I even married a Republican. Yet here I am, a liberal college professor at a Jesuit school who still isn’t baptized who teaches a course on culture, racism, and health of the LGBTQ community. My parents are still super proud of me!
But yes. I shut my mouth at home until I got out of college and was living on my own. I happily did my own thing outside of the house. I didn’t lie to them but I did just excuse myself from conversations.
To this day I can’t follow my dad on his social media because I get too frustrated with him!
Your parents likely mean to have good intentions. Their values are important to them. As you age, you may grow into your own beliefs but who knows, you could be more in the middle than you (or they) think! Right now your parents just struggle with thinking like you will purposefully go against their beliefs. Im a mom to 3 kids, 21-17-15, and it isnt always easy letting them be their own people. Parenting is a journey!
What about the University of Rochester? Merit aid, the right size, in a small city, very strong in stem and music! Plus there’s got to be skiing nearby with all that snow. No more liberal than any other University. You would bring geographic diversity to them as well.
The presidential scholarship is a bit better than that because the OOS scholarships (other than WUE) encourage you to get residency after the first year.
First year you get $20K off what is about $30K-$35K in tuition plus $5K off the $15K room and board. After you switch to instate you get $12K (which is effectively full tuition) plus the $5K off room and board. So net cost (excluding travel etc) is about $20K to $25K the first year but only $10K in subsequent years. That’s as good or better than full tuition in many other places.
Note that the Eccles full ride is now limited almost entirely to instate students.