It’s a good example of an issue that is not a simple binary two-“sided” thing.
There are probably specific exceptions, but in general I would say both positions have merit:
1) An employer (or school or other organization) can be allowed to specify a dress code as a condition of employment (or participation in certain activities).
2) In situations where mostly there is no dress code, then religious garb should be allowed.
Those are two separate things, though, and yes they can overlap and be at odds.
In general there should not be dress codes that aim to exclude and marginalize some groups or religions over others, particularly in a place like The United States of America is supposed to be, where there is supposed to be no official religion and freedom of religion is one of the main principles on which the country was founded and which many people still cherish.
In France, however, there is a vastly stronger traditional position of French Catholicism as the dominant religion, which is opposed both by secular humanist positions, and challenged by France’s history of colonialism and it’s non-Catholic minority population. That situation makes the example in your second link much more charged, complex, and specific.