I believe their hostility towards Americans is determined by the wide-spread antiamerican propaganda in the Russian mass media. Thus, it's highly unlikely that it has something to do with American mentality or simple American people. Even if so, prove them wrong. Show yourself friendly, polite and intelligent. Treat them with respect. Be a good company, make them sure your relationship with their daughter is serious (without demonstrating your emotions publicly) and that you have promising prospects. If possible, ask your girlfriend about their jobs, views, hobbies and tastes before you meet them. Besides, it may be a good idea to cover your tattoos :)
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"