It is a very interesting question. And I'm afraid it has never a convincing answer for all cases.

Nobody I think would extend tolerance to religions (or local faiths) that demand human sacrifices like for instance widow burning. But in between there are so many difficult cases. Some instances from Germany:

Muslim women who demanded that their faces were not photographed for passports (except for an eye slit). Denied by courts
Teachers who demanded that they could show their religion by their choice of head cover (Sikhs, but not only them). Denied by courts
Muslims who demand that their method of slaughtering animals which is in violation of German animal protection laws should be allowed. Granted by courts with the restriction that the animals have to be anaesthetised. Not accepted by (some) Muslims who claim that they have to kill the animals with them feeling the full pain. Still pending.

Some restrictions seem to be plainly silly. For several years, the rules in Olympic gymnastics made some prescription on what to wear (and hairlength, I think). Sikhs could compete but had to suffer a deduction of points for the way they looked. Silly.

Less silly would be the same decision in professional boxing or in other sports that demand a certain type of head cover (cycling, ski racing, motor racing).

I'd say in those cases the person should choose another sport or profession.

Wolfgang