When I met my parents, I found that my father-in-law likes to secretly beat and scold her mother-in-law, which shows that this family is patriarchal and has a low status, right?

This shows that your father-in-law is a strong figure in this family, a little male chauvinistic and disrespectful to his mother-in-law. You should carefully observe your boyfriend, whether he is influenced by your father-in-law, and whether he thinks you are right. If he is a little bit, you will have a hard time in the future. You'd better be careful about this.