The LDS church has covered up sexual abuse as well.
There have been several publicized cases lately.
There was a serial rapist in my LDS congregation, the Stake President (similar to Catholic Bishop) knew about it, covered it up and kept moving him to different wards after every rape. The women were counseled not to press charges because he was ‘mentally sufficient’ and therefore didn’t know it was a sin.
His psychologist (also LDS and the father of my then boyfriend) broke doctor/patient confidentiality by telling me what was going on and warning me never to be alone with him.
AFA child brides, SLC stopped that practice in the 1930’s, although as late as the 1990’s you could get married at age 14 with parental permission and I know 4 girls who did (all the husbands were over 18, one was over 30, and all were LDS).
That's a function of the State, not the church. For example, in New Hampshire you can get legally married at the age of 13.