I don't know if sexism and racism are so easily pulled apart, AF Mind. For starters, let's just keep to the United States of America.
In 1662, in the Virginia colony changed the law regarding the status of children. English common law had always maintained, that under the law, a child takes on the status of the father.
Okay, clearly a sexist law by a sexist, patriarchal society: England.
But the 1662 Virginia alteration provided for a child to take on the status of the mother.
What's going on here? Was sexism suddenly wiped out in British colonial America?
Hardly. This changed was connected to slavery. This changed favored male, white slaveholders who had a tendency to rape their black female slaves. With the status of the child now legally affixed to that of the mother, the plantation owner had no obligation to the child. He didn't have to free his children sired in this way; and indeed, they were simply added to the slave workforce.
It was "sex without any long-term consequences," as it were, on the part of the white male slaveholder.
One can say that, to this day, and in this way, sexism and racism are interacting, overlapping, and mutually reinforcing. America is the land of the so-called "one drop rule."
In America, then, through the woman (the enslaved woman), blackness is a was conceived as a sort of Eve's "Original Sin," that forever tainted the blood.
Consider the infamous case of Plessy V. Ferguson (1896).