Does Baseball Hall of Fame have character requirements for eligibility?

[RgrF]

Ty Cobb was not only a virulent racist, he was the Ted Cruz of baseball. He was such a miserable person and dirty player that he became the most hated player of his day. Despite this he was an almost unanimous pick.

If he can be in the HoF then Schilling, Bonds and Clemons should be as well. Maybe set up a separate wing of great players who were bad people?