People that are rarely aware of their bigotry, whatever that prejudice may be, and it is not entirely their fault. Often, it is the result of cultural influence on them. They grew up in it as their basis for judging "normal" from "different," and unfortunately, for conservatives, better is not based in what improves mankind but allows it to walk backwards in time to a "simpler day" in their mind...which really means not having to challenge their prejudices or to change.
How they treat women are examples of this, as is how they treat former slave races in their states, how they treat Union states, how they treat other countries, how they treat children, and etc. But, for women, it means getting back to the simpler days, when the "Divine purpose" for women was to bear children and be silent and submissive to men.
If you think that is an over exaggeration to make it sound like handmaids tale,consider this, which they consider to be the "infallible word of God"...
"Women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church." - 1 Corinthians 14:34-35
"I do not permit a woman to teach or to assume authority over a man; she must be quiet. For Adam was formed first, then Eve. And Adam was not the one deceived; it was the woman who was deceived and became a sinner. But women will be saved through childbearing" 1 Timothy 2:12-15
So, it is no wonder, then, when the GOP President's response to them is to grab them by their privates and the "Pence Rule" counter is to just not be alone with them. BOTH are symptoms of the same illness of prejudice that doesn't answer with... Just see them as equal people, because GOD tells them, in their mind, that they are not.
Prejudice does not disappear easily and will likely not change in those that have it. The BEST we can hope for is to keep them from positions where they can use it.