Same with the tenants. I might prefer to rent my property to a woman because she takes care of the place better and is less likely to throw a party. Is that a discrimination?

Point is if there's an objective reason behind it then it's hard to consider it discrimination, even if it segments the groups on race/gender/religion.

In the case of prospective tenants, I assume a fair degree of self-incrimination would be required to prove discrimination based on a protected characteristic.

To the point about some people's rights being "more important" than others', rights are a zero-sum game.

Giving protected classes a right to service from businesses necessarily comes at the cost of business owners' rights to refuse service.

The law is necessarily concerned with determine whose rights are "more important" in these cases.