It is possible to encounter prejudice, racism, and xenophobia in the US, but these things are not as common as they used to be, or as harsh and overt. They would tend to be directed toward specific groups who have historically been oppressed in the US. The realistic concerns for travelers would mainly be:
A traveler of African descent might encounter racist reactions such as being followed in a department store by a security guard, or taxis not stopping for them.
A traveler who looks Latin American or who speaks Spanish might be harassed in areas near the Mexican border or encounter racist reactions such as an assumption that they are uneducated.
Although some areas of the US are ethnically homogeneous, in general it's a nation of immigrants, and people are used to interacting with foreigners.
California is a huge state, and it has many different regions. The big cities are very cosmopolitan and have large populations of relatively recent immigrants. Areas like the very far north are rural, and people there may simply be curious about a Russian traveler because they've never met a Russian.
I doubt that anyone is going to blame an individual Russian citizen for Putin's behavior, just as I would hope that nobody in other countries would assume that I was in favor of invading Iraq just because I'm an American.
America does have a legacy of anticommunism and Russophobia because of the Cold War, but most Americans realize that the Cold War is over and the USSR no longer exists. For example, I'm 49 and I have a collection of Fantastic Four comic books that date from the 1960's, when I was a kid. The superheroes talk about the "reds" and how we have to beat them in the space race. My teenage kids read these stories and find that material funny and out of date; for them, it's like something from a history book. Americans will probably not remember what happened in Ukraine by the time you visit California, since they don't really care.