Curt Schilling's ability to pitch cannot be denied. His playing career was Hall of Fame-caliber by any reasonable argument.
Rule No. 5 for election to the BBWAA is voting and states the following, "Voting shall be based upon the player's record, playing ability, integrity, sportsmanship, character, and contributions to the team(s) on which the player played."
The character clause is what's coming up now, again. Schilling's anti-Islam and anti-transgender stances are well known, and many don't want him rewarded with a spot in the Baseball Hall of Fame.
However, Schilling's character was never called into question during his playing days.