I am an Asian American, and I think putting Asian on my college application will harm me. Are there any downsides to not filling out what race you are?
I thought this too (I’m asian too) but I looked at the schools and realized I wasn’t really too much at a disadvantage? Most schools 20-100+ rank were something like 50%+ white and only 10-15% asian so its really not that bad. I don’t know if race is optional to fill out but you should definitely fill it out because statistically you would have more chance filling out asian rather than not, wherein they would probably just assume you were white 
Top schools have a large amount of asian americans due to higher test scores, academic performance, etc. The pool is much stronger for asian americans in general, so affirmative action exists to create diversity within schools. That being said, I think you should always state who you are.
It makes me sad that you this is even a concern for u guys.
It’s a sad reality that race is a factor in college application, unless your target school is a public university in one of those eight states (including CA, MI, WA) that explicitly ban racial consideration.