Am I still allowed to like them?
Yes. No one is stopping you from doing anything. You can like and consume their work without liking them as a person. You can even like them as a person, so long as you recognize that they do have problematic issues.
How can I be a good fan?
Try and make them a better person. If they do something problematic, call them out on it. I recognize that famous people are busy and don’t read every single Twitter reply or Facebook comment they get, but still try it. At the very least, you’ll be educating other fans.
How can I be a conscious fan?
Recognize that they did something wrong. Accept it. Don’t try to defend it or explain it. Say “so-and-so makes great music, but I wish they weren’t racist” or “I think that they’re really talented, but they are also sexist”. It’s a package deal. Tell other fans what they did. When praising them, don’t ignore the problematic stuff. Talk about that too.