I wouldn't want my children to go into a school bathroom, either ... but more expensive soap isn't going to address the real problems!
It'll make little difference when the kids haven't been taught by parents to wash after usng the facilities (at school or at home).
the grammar school my kids went to, hadn't been repaired or upgraded since the 40's. The boys bathrooms had no doors on the toilets
The little boy I watched after he got out of school and my son would come in and sit on the toilet for quite some time every day.
One of them got hemmoroids. I considered this a form of child abuse. I went to Social services to report it, and they scoffed at me saying the schools had no money to fix it.
If I had a bathroom at home in that condition, the same Social services would have no problem with removing my chidren from my home.