Well I’d have the same objection if the coach (or even just a group of the players) wanted everyone to look like anything, not just Aryans – that’d be something else.
There can be several aspects to it. Another would be maybe people joined the team under one set of agreements, and then suddenly the coach insists everyone does something semi-permanent to themselves that has practically nothing to do with the game. So it’s an unjustified and unexpected changing of the contract by requirement to do something after the players have committed to the team.
And then there’s the whole aspect of peer pressure, and of athletic director excessive authority overstepping boundaries (which is definitely “a thing”).
And there’s also the assumption everyone is happy and comfortable changing their appearance to be like everyone else and that being required/obliged/pressured into doing so will increase loyalty rather than cause resentment.
All that stuff. Of course, just signing up for organized sports teams tends to involve a lot of surrender to various forms of discipline and obedience, so many may go along, and resistance or speaking out against it is probably greatly discouraged in various ways. Adding hair dying is another layer on top of the others, but also seems excessive to me.
Of course as @Dutchess_III mentioned, if they just mean to use something that washes out, that’s much less intrusive.