Your own study does not sorry the claim.

(1): There is no mention in the methodology of any examination or study linking male presence with children with sexual abuse. There is one training from a male teacher saying he's not allowed to go into the girls locker room or help them undress because that would be seen as pedophiliac. Comparing that to being around your own children in public is a false equivalency of severe magnitude. I can't go into a boys locker room and help them undress in America as a woman either.

(2): There's no eyewitness evidence of the male teachers being falsely accused of rape by teaching children. The article had two testimonies from two male teachers afraid of being profiled because one male teacher did rape one of his students. There's no proof they were profiled or fired or harassed though.

(3): The overall study showed men have trouble breaking into traditionally feminine roles, something which no one contested. You don't have to go to Brazil for that kind of study, it's right here in America too.

That is not a study showing men are profiled as sexual abusers for being with their kids in public though, and that was the original claim.