Next year is Sophomore year, and I plan on taking Honors in everything except math, where I will be taking regular Geometry which at this level is a step above Algebra 2 but still below those taking Honors Adv. Algebra. Will colleges not care about about this as long as I mantain an average A? I’m already planning on taking Honors Chemistry and Accounting so it’s not like my schedule is gonna be void of courses involving math.
You’ll be fine taking regular as long as you get an A. But why not take honors? At my school there is not that much of a difference, and if you are taking honors everything else, you should be able to handle honors geometry. I made the mistake of taking regular geometry and it turned out to be a joke class and overall just a waste of my time. There is no reason not to take honors unless you just struggle with math.
My School is rather strict with prerequisites for classes, back in 6th grade they would either place you in Honors, middle, or acedemic for your seventh grade year depending on performance which had a snowball effect on what classes you could take later on and since I’m in the middle, I can’t just choose to take the honors level class. It’s real stupid.
If you’re taking honors everything else (especially English and social science/history) and only have math not honors you’re ok as long as you get an A. 
Hmm, can you over ride the school and insist on honors math? The only reason I say this is that regular math may prevent you from some science and math classes down the road ( which are frankly more important) than geometry.
^ Op has already explained that’s what happened
For an over ride, op needs his/her parents cooperation advocating g persistently till op is put in algebra2+ geometry honors to catch up. But if OP was placed on a path that leads to precalculus, that would be fine.
My path goes like this:
Regular Algebra 2 —>Regular Geometry —> Regular Trig/Pre Calc —> Pre Calc 2 or Calculus (I COULD potentially take AP Calc if I end up impressing my Junior Trig teacher, ironically AP Calculus is the only high level class that is not closed off to only honors students)
Then you’re 100% fine. If you can take calculus or AP calculus, youre good to go at all colleges (yes, all of them).
As long obviously as you take mostly honors classes in other classes, can take 4 APs in core subjects ( like English language, literature, history, economics or government, foreign language…) and get good grades overall