Would I be accepted?

its deeper than that
you can be a better native speaker than the natives and still be a foreigner

>nobody will "see you as one of their own"
Not exactly true. But that depends on him

>If I were to go to one of these countries would they see me as one of their own or as an American.

In Russia you'll always be considered an American, your "ancestry" does not matter if you're born and grown abroad.

I can speak English, but it doesn't make me an Englishman.

No. You would be just another generic American. Even 100% percent Russians are seen as foreigners if they were born and raised in another country. You are a lost cause, matey.

I meant my parents are from Serbia and Russia and I was born and raised under the culture and identities of each nation

>your "ancestry" does not matter
This is what amerimutts never understand

I mean I don't really want to be Russian or Serbian and am fine with being an American. I was wondering if they would see me as either one.

You got your answer then.

>I was wondering if they would see me as either one.
Why would they? You are American and you will be seen as American.

Would you consider a Syrian born in Germany to be a German then?