I was in Moscow briefly 4 days ago (and in Russia for a week) and didn't feel unsafe because of being from the US. I would just use common sense - refrain from getting into loud heated arguments with people over Russia's role in Ukraine (unless you know them) or walking around Red Square with anti-Putin signs. Remember than the Moscow subway shuts down at night and some areas outside city center are not safe at 3am. Some people, although they are rare, still believe that Americans are all rich and money grows on trees, so don't flaunt $10,000 unless you're at the GUM (big Russian mall), where that money won't buy you parking space, lol.
But if your main worry is whether regular Russians dislike regular Americans...I didn't find that to be the case.