Racism is absolutely still a problem in America. It always has been and likely always will be.
Unfortunately, it seems like it's just ingrained in humans subconsciously that we need to group ourselves and one group has to be better than another. It's sad.
In America it varies from city to city mostly. In my city it isn't much of an issue (to my knowledge) but in big cities like Dallas where there's riots, it is clearly an issue. I think anyone claiming racism isn't an issue in America is just ignorant to the issue.