“By saying that halachos and minhagim stated in chazal can be attributed to bigotry against women, the entire concept of mesorah falls.”
Wait a minute. There is a big difference between “minhagim” and “halachos” here. How is the concept of mesorah harmed by saying that minhagim were influenced by bigotry towards women?
Furthermore, if by bigotry you mean sexism (as opposed to misogyny) then they are correct. Many halachos are sexist (e.g. a woman cannot be an Eid for many matters). As long as that doesn’t mean that the halachos are invalid, how does it damage the mesorah.