And then there is the uncomfortable truth that equality and liberty are in opposition to each other. Liberals allegedly believe in both, but the one will always suffer at the expense of the other. Usually it's liberty that suffers. Today's liberals tend to be quite illiberal when it comes to the freedom of conservative reactionaries to choose with whom they wish to be associated.
It depends on what you mean by equality. Equality under law, or equality of outcome? Equal liberties and responsibilities, or equal distribution of wealth. The former seems to me to be liberal. The latter seems to be anti-liberal. Those who prefer equal outcome and equal distribution are not truly liberal, in my opinion.
I certainly don't oppose equality under the law. The problem with equality as a political ideal is that it goes beyond that. It ends up coercing people to do what they would not freely do. I have no sympathy for a White bigot who won't hire or serve a Black man. On the other hand, I totally sympathize with the Christian school that won't hire a man who claims to be a woman. In light of the recent Supreme Court decision written by the "conservative" Gorsuch, will Christian schools retain the right to exercise their religion in hiring and firing employees? Or will their freedom of religion be sacrificed on the altar of social equality?
I think what you are describing is illiberal, not liberal. I have been arguing that "liberal" is a misnomer when applied to the American left.