...children who are homeschooled are not “socialized” by association with other children.
So take ‘em in the bathroom, beat them up, and steal their lunch money.
I've not seen any statistical studies which tell me that homeschooling is motivated by the existence of integration in the schools. Interestingly, the same argument applied to sweeping away Plessy vs. Ferguson (separate is permitted if equal), socialization (integration and what it is believed to produce) is important and socialization in the school is important for stay-at-home kids. In the absence of data, it is not right to equate the two.
It seems that the tests and standards always run in one direction: It is not a test justifying homeschooling that the child is unsafe in the bathrooms but it is a test of the particular home school application if the parents harbor firearms or failed to maintain required records. Just as the idea of association as applied to homeschooling is a one-way street: important for socialization in general but not for socialization which might occur on the playing field.