Sexism is defined as preference of one gender over another, prejudice for one gender over another, discrimination of one gender over another.
While it's true that women face significantly more sexism then men, sexism against men still happens in certain cases (breast cancer care, for an example). What you've just described is certainly sexist. Whenever you're in doubt, turn the situation around. If someone told you that there is a time when only men can go in, would it be sexist? It would. Just like this is. As a male, I would be angry to know that there's a "male-only" slot of time.
As far as religion goes, no one should care about your religion. Literally no one. People can be religious, but our society at large should be secular and assume secular values. This means that no policies and rules should be instituted to recognize certain or any religions.