I'm not saying it's political speech, I even mentioned commercial speech in there as well. I'm just saying that in a professional sports setting, it should be about the game, not whatever social, political, or economic issue the player is interested in.

No more mention of the player's wives and children

Agreed. I don't see any reason for a player to have their wife or children displayed on their sticks or anywhere on their uniform while playing. If there's a section for a bio somewhere (like when they're being announced coming onto the ice), it could mention their support for LGBT issues or their family life or whatever. They'd get a small blurb that can say whatever they want, perhaps audited for hate speech or commercial ads that are in conflict with whoever is advertising for that game.

But I don't really see any reason for players to be advertising anything on their sticks or jerseys while playing. Whether a player is LGBT or supports LGBT issues should have no bearing on how they play the game.