No I can’t cite a US regulation that classifies just being a Muslim as some sort of criminal act and/or grounds for denying someone their civil rights.
No, no one said being a Muslim is an impairment.
“Or legitimate grounds to deny someone service” Bingo, it sounds like it in this unique case.
thetruthaboutguns.com/2014/09/robert-farago/officially-declare-business-gun-cave-indoor-shooting-range-muslim-free-zone/
Game over, it is up to her discretion. Looks like you have to take it up with the ATF and Federal Gun Laws.
Now, you can argue that she is being prejudicial and many would agree with you and you can argue that she is in the right and many would agree with that.