Why does anyone have the right to make others support something they do not believe in? Americans have the right of refusal regarding religious freedoms and individual freedoms. As I fully support gay marriage, and always have, no one has the right to force beliefs on others who do not agree. It's total nonsense.
I actually agree with you on this. Although these ballplayers are in the entertainment business and the last thing such businesses want to do is piss off their paying customers (fans), making a ballplayer wear a rainbow jersey infringes a bit too far on his First Amendment "free exercise" rights. Maybe just have that player sit in the dugout or the clubhouse for that game. If he doesn't support the gay rights or Pride Month (which are pretty close to being the same thing), then just give him a day off. If a ballplayer had previously signed an employment contract agreeing to support the ballclub's promotional activities and "Pride Month" activities were included in the list of promotional activities, I would probably feel differently.
The San Francisco Giants have a bit of a PR mess on their hands right now, after four of their players put a verse from Genesis on their rainbow logo'ed hats to indicate their non-support of Pride Night. Aside from the fact that a meaningful segment of the Giants' fan base is gay, a much larger segment of that fan base is composed of straight folks who are supportive of gay rights and Pride Month. This is San Francisco we're talking about. Those four guys (and the ballclub) would have been better off if they had just quietly taken the night off. That seems a reasonable compromise, whereby they express neither support nor antipathy.
These "free exercise" cases can be thorny. A person's religious views obviously merit considerable First Amendment protection, but sometimes they run up against other interests that also merit protection. Such as protection against discrimination. The cake baker dude who sued so that he could deny service to a gay couple seeking to have him make a wedding cake is a good example. That guy was and is holding himself out as offering his services to the general public, so I think his "free exercise" rights do not give him free rein to discriminate against particular segments of the general public. But I would also acknowledge that it is a subject worthy of debate. There was a restauranteur in Oakland who, following a controversial police shooting incident, decided to express her First Amendment views by putting up a sign in the front window of her restaurant stating that she would henceforth be refusing to serve OPD officers. Leaving aside the fact that it seems pretty dumb to antagonize the very cops who are charged with protecting you from possible criminal activity, these cops are likewise members of the general public, and it seems discriminatory to refuse them service solely on account of their occupation. I see parallels between these two cases.