I respect your right to run your business as you so choose. Of course, if how you run your business somehow offends me, I also have the right to take my business somewhere else.
Do private businesses have the same right? Do businesses have the right to deny service to those they judge to be immoral? Let’s say you find 1) hate speech, 2) religions that oppress women and 3) homosexuality immoral. I wonder, would the commenters on here respect your right to deny service to all three?