Generalizations about misogyny in various cultures are often lacking. All cultures, that I know of, contain forms of misogyny and racism, and other bigotries. All cultures have the ability to change.

The right wing has often had members telling other members to ‘welcome the Hispanics, they have deep-seated values like our own, from the church’. Most Hispanic culture in the SW US comes from Mexico. In Mexico, they had a couple of revolutions. (Some priests were leaders.) This is from 1991, things may have changed:

Under the constitution in 1917, which is still in effect, nuns and priests are forbidden to join political parties, vote or wear clerical garb in public. The constitution banned parochial primary schools and religious ceremonies outside church buildings.

Mexico recently made abortion legal. The medication version is over-the-counter.