I agree. I mean, I do think "daughter of two Iranian immigrants, grew up in New York all her life, currently a college student studying anthropology" is plenty interesting on its own. There's nothing wrong with simple and straightforward. Also, anthropology is fun. :P

I do think that introducing parent/daughter cultural differences and incorporating some of the current prejudices would definitely add onto that foundation though. It seems likely that even if you don't want to make it differences on the Iranian cultural front, it could still very easily be generational culture. And it's always good to include the personal effects of a global issue when it's something that would have an impact, more or less, on all the characters involved. It could definitely add further dynamics to character interactions during downtime. 

So, go for it if you want. :)