Most people agree that it is wrong to discriminate in commerce, employment, and housing, but is it wrong to discriminate in personal intimate relationships?

Most people agree that it is wrong to discriminate against people due to race, gender, religion, sexual orientation, etc. in housing, employment, commerce, etc.

But what about personal intimate relationships? Is it wrong to reject someone as a possible sex partner for reasons of race, religion, gender, sexual orientation, even if you otherwise believe in equal rights and equal opportunity in employment and commerce?

For example, is it wrong for a heterosexual male to reject a homosexual male as a potential intimate partner? Is it wrong for a Christian to reject a Jew as a potential intimate partner? Is it wrong for a cisgender male to reject a transgender female as a potential intimate partner? Is it wrong for a white person to reject a black person as a potential intimate partner?

I.e., should people be allowed their personal biases in intimate relationships, that are not (and should not) be tolerated in public business relationships?

Donning my flame-proof undies now :-p