So long as the prayer room is available to all faiths and not just one, there is no problem with this.
If it’s a private company, they should be able to do whatever the hell they want. As a country, we should require that our government prohibit individuals from entering it who are so entirely incompatible to the core of our beliefs.
I think I remember reading that Muslims don't allow infidels into their mosques. They probably wouldn't be as accepting as you, FRiend.
Your idea was tried at some college in MN, iirc.
There was a problem: The Muslims didn't want to share the room.
A compromise was tried, with a curtain or temporary wall dividing the room so that Muslims could have their "own" space.
IIRC the Muslim students were not satisfied with that arrangement and continued to demand an exclusive room for their "worship."