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.
