If someone walks into a business with a menacing look on their face and is refused service, is that discrimination against people with menacing looks on their faces?
Should businesses be allowed to discriminate against polygomists? Or pedophiles?
Sounds like a lot of work deciding how to police these businesses. I guess the government doesn't mind because they want to control everything everyone does all the time. ... Or, you know, we could just let businesses decide who they want to do business with.
It's legal to refuse to do business with any individual. It's illegal to refuse to do business with an entire class of people, simply because they're a member of that class.
In Arizona being gay is not a class. So this law is attempting to solve a "problem" that doesn't actually exist.
In terms of religion, there's a big difference between beliefs and practices. Any and all beliefs are legal in the USA. Practices must exist within the law.