Yes, you 100% need to assimilate to the culture of the USA - we are supposed to be the "great melting pot" but you don't feel that need.
If you don't want to do that... just stay in your home country.
Also, Islam isn't compatible with the West but you already know that.
Should a minority community's right to be in America depend on their willingness to converge with the cultural mainstream? No, it shouldn't depend on that. It shouldn't depend on anything. We're all Americans, after all.