Me and dh have a very equal relationship. Dh does loads around the house, we both worked full time, both do equal childcare etc.
My kids (a Ds and Dd) still come out with stuff like this.
Both me and dh gently challenge why they think it.
Ds came home sayin she needed a new lunch box because hers was a boys. She wasn't upset, she took it as fact. So we asked about why she thought it, that she picked it because she liked it, why can't she like that character because she is a girl etc?
I then spoke to the class teacher, who agrees any kids saying things like tags should be gently challenged and she did a talk with the class about sexism in a age related way.
Ds (5) sometimes says things like 'only boys play football' so we watched women's football, asked him how he would feel if someone banned his sister or me from playing football with him. He agreed the 'boys can only play football' was silly and we extended that to all sports and everyday life.
Dd recently was told she couldn't be an engineer, by a boy at school. She wants to work for Airbus. They are at secondary. She asked him which part of an a330 was built using a penis 
In short I don't think your set up has caused this. My kids seemed to pick it up at school. What is important is that you challenge it and talk it through, with him.