What about discrimination by private entities?

It is important to note that nowhere is discrimination against every category prohibited. Nearly all businesses would turn down certain types of customers. Only discrimination against certain protected characteristics, usually (but not always) immutable ones, irrelevant to the business, is prohibited.

In a democracy, the passing of a law prohibiting discrimination against a certain group requires the majority to be against said discrimination. This means that this group won't be discriminated against by most people anyway. Those that do will suffer losses from missed customers. People strongly opposed to the discrimination may even counter-discriminate, boycotting those that do.

In such a situation, it doesn't seem all that necessary to legally prohibit discrimination, especially to libertarians, who believe that no one can be forced to serve another for whatever reason, even "social justice".