Don't be afraid. Some russians may declare hate, but in personal communication they forget about it. They hate "any american" (in general), but will love "the one american" probably. If you have money, or job, or some property — you can ensure your girlfriend(wife), family. That is really important for russian parents. Tatoo is pointing that you are out of old society norm, but if you have good job — it is OK, you are fit in expectations. College or some education is good too. Big family, knowing your ancestors is good. You can always say "I am american, but my grand-grand-parents from Germany(Europe)".
I'm sure they don't really hate ordinary American People. But if they're the kind of people that really hate a whole nationality, I wouldn't waste my time trying to win them over. Life's too short to deal with assholes.
Brace yourself! I am still easily swayed by my parents' opinions. If you live in America and are going over there for a visit they expect you to bring gifts "gostintsy"