Probably not everyone has the wherewithal to do what I am about to propose, and possibly you do not, and that is fine.
The real issue at the bottom of your problem seems not to be that people are very curious, or that you are very private, but that many folks really want to draw conclusions about you as an individual using stereotypes of geo/politico/cultural groups that they can associate you with. Perhaps this is because, as is often the case, they themselves identify their self by the groups that they belong to. Being from the Southeastern USA, I get this all the time from sports fans: Joe is an Alabama fan, and that is who they are. They want to know who am I, and by "who am I" they mean what sports team I follow, because that is their conception of the self.
This brings up some possibilities for dealing with the root cause of the situation. The most basic retort, then, is "I was born in Russia, but that is not what defines me as a person. I am glad that you would like to get to know me better. What would you like to know?" This gives you an instant opportunity to simply disown any uncomfortable questions that they are asking, to let them know that you're not interested in these lines of questioning, and that their attempts to find out about you are actually failing because they are asking the wrong questions, not because you aren't giving any answers. I, for instance, can respond to Joe by saying "I'm not into sports." Joe may easily interpret this as me being some kind of soul-less robot, because by "self", Joe means "what sports team do you follow." If I'm okay with that, I can leave the conversation there, and Joe will cease to ask me "personal" questions. If I would like to have some kind of relationship with Joe, I will have to disabuse him of the notion that because I don't follow sports I have no soul by showing him that I am. "I'm not into sports - I'm into art. Allow me to tell you all about art!" Possibly Joe doesn't care about art and doesn't want to have a relationship with me, the artist. This is fine, and I cannot force Joe to accept me for who I am, but at least I know who Joe is (an Alabama fan), Joe knows who I am (an artist). There is no illusion on Joe's part that I am some kind of secretive Tennessee fan who is out to get him.
People who are asking you about where you are from, and your relationship to that place/nation/people are trying to find out more about you. They are interested in you. If "Russian" is where you were born, but does not describe your self, then tell them that. It may be hard for them to understand, because Jacques is French, and French is what Jacques is, so that when you tell Jacques that you were born in Russia, but that "Russian" isn't what you are, it requires more than superficial explanation. But, you are a whole person, and I'm sure you can tell Jacques all about the things that you are, without having to elaborate on the things that you aren't.