I mean, if you want to try and debate whether someone's individual stance is right or wrong, take that up with them. But rightness or wrongness doesn't necessarily equate to someone being allowed to hold a private opinion. That can't be the standard.
If she had said it on the air, or on stage at an ESPN event or something, that's different. I don't think Capitol Records needs to clarify that it disagrees with what one of its artists says in a song. Let her apologize if she wants, let her deal with the blowback online, let her further address it on her twitter account, etc., but it wasn't related to her job and wasn't while she was working, so ESPN bears no responsibility for it.
Now, if they want to decide that the outrage created is significant enough that it will cost them viewers or revenue or whatever, they can encourage her to get out in front of it. Or if it does ultimately destroy her ratings/career/credibility, then they can let her go. But no one actually thinks ESPN holds all of the views of its independent personalities simultaneously.