Edit: I'd also say that the ban on rainbow tape was clever because it is setting up the reverse situation. Now, we can have players getting in notable trouble for going against the league and using the tape anyway. I bet the league wants it to happen and for it to get press
If it actually has this effect, it could be positive for the league. Just wait until certain publications out there highlight the players who use the pride tape, and watch all the people who get irrationally upset about a bloody rainbow on a stick blade for ten minutes once a year before a game.
In my view, the league loses no matter what it does, but it stands to lose a lot less, and maybe even continue attracting interest from people who weren't all that interested previously, if they're open to players using pride tape and teams wearing pride sweaters during warmups.
I know several LGBT+ folks who are unhappy with the league and its decision to ban pride tape when they themselves were attracted to the sport because of it, and the perception of inclusivity. By taking a stand against it, they're not just alienating the people who were interested in the sport because of that, but also undermining their "hockey is for everyone" marketing.
Time will tell whether this has any effects on the league in the long run, but I think the league would've been far better off had they simply not taken a position on this issue.