If we want to use sports analogies we don't have to use Nike and Adidas as stand-ins, golf is undergoing this right now, between the PGA and LIV tournaments, and members with exclusivity clauses in their contracts.
LIV doesn't forbid their golfers from anything, as far as I know. It's the PGA that banned LIV golfers, not the other way around. LIV golfers still compete in non-LIV, for-profit tournaments that aren't part of the PGA Tour.
Or the 80's USFL (United States Football League). But these alternative leagues do kind of color the analogy in a way that might be slightly muddying -- I mean, come on, the PGA and NFL are the prestigious competitions in the eyes of the public. Is one of Lichess, chess24, or chess.com an assumed pretender?
It'd be more like if Lichess were funded by Nazi gold or something, and the person funding it was trying to do so because they want you to forget they stole a ton of Nazi gold.
PGA isn't behaving this way for moral reasons, but it's an extra component to that situation which makes this harder to analogize.