At this point, Wiggins does have the "right" to choose to be unvaccinated but if he makes that choice, he also has to accept the consequences. In this case, his employer has determined that it is bad for business to have their star athletes catching and spreading the virus so they have exercised their right to require their employees to be vaccinated.
I don't think the NBA/Warriors should be forced to accept a religious exemption, even if it was real. Say someone worked where it was necessary for cleanliness reasons to not have long hair or a beard. If a person claimed that their religion didn't allow them to cut their hair or beard, should that company be forced to continue to employ that person?
Wiggins will be creating a less safe environment for other employees and customers. Why should an employer be forced to accept that even if the religious objection is legitimate (which in most cases it probably isn't)?
And as to masks, they significantly reduce the spread of the virus from an infected person to the rest of the world. Masks offer some limited protection for the person wearing the mask from getting infected. I am surprised people are still poo-poo'ing masks.