I think you are correct as it is now. And I do agree, as it is right now it is not practical to be completely secular for people holding these offices.
However, ideally, these groups would not need the recognition in this way as they ought to already have it otherwise and understanding that at some places some things are limited, should not discourage them to believe in what they want.
Similar to the original meaning of this post. Many countries forbid people to enter the military and similar office, if they are known to hold extreme believes (e.g. extreme right wing rhetoric has been used by them or such). Not always foolproof though