We prohibit discriminating customers on the basis of color. religion etc. Add one more clause: discrimination based on political/social beliefs or something along those lines however stupid those might be.
That's a terrible clause. Half the point of free exchange of information is so we can find which deeply-held beliefs (which are maleable, unlike color) are incorrect, detrimental, or even dangerous when acted on.
Black people and pedophiles don't deserve the same legal protections to have access to a playground or a private school.
I don't think it would make much of a difference. Are there pedophiles who publicly post controversial views without the cover of anonymity? How would you even know what their views are?