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In my experience it isn't rudeness, but a different cultural standard. Amongst Americans, we do not find it acceptable to display non-positive emotions publicly. You're allowed (and encouraged) to smile at everyone and seem like you're always happy, but if someone you don't know very well pisses you off, you aren't supposed to tell them so. That's a negative emotion and so you're supposed to repress it until you're in private.
To Russians (and amongst other Eastern Europeans) this is considered fakeness and this kind of behavior is looked down upon. In this cultural standard, people do not have a problem with letting others know when they've done something that has made them mad, even if that may occur in public. In my experience this isn't usually done rudely, by calling a person names or something, more along the lines of saying "Why did you have to go and do THAT?!?" and expressing frustration non-verbally.
The best way to react (the way people who have grown up in that cultural standard react) is to not take it personally, because it isn't personal. Just shrug it off and say nothing or say, "Well, I'm sorry you're upset." That would be appropriate if you've done something that a person doesn't like, but that isn't actually wrong.
If you have actually done something wrong (spilled coffee on someone, stepped on someone, etc.) better not to say that though, and to actually apologize for what you did. If the person is still angry after you've taken appropriate measures to apologize and correct the situation if necessary, again, shrug it off.
About women: young, attractive women all over the world are sometimes rude as a defense mechanism. They are very used to men who are complete strangers trying to get in their pants, and one becomes weary of such a thing. This is no different for young, attractive American girls. You may find that this happens even if you behave like a perfect gentleman.
I think it's difficult to compare rudeness levels between Americans and Russians because what is considered rude is not the same. In some parts of the States going about in public with a sullen expression on your face is considered rude, whereas amongst Russians, hey, that's just your business, nobody cares. Furthermore, what's considered rude in America is not the same everywhere. I'm from Texas, and I can assure you that what's considered polite there is very different from standards in New York City.
To your last question, I'm an American, I live in Europe.
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