The de facto rule is closed toe shoes in those particular classrooms.
Up to about ten years ago there was a mobile phone ban in the school. It had been in place since the dawn of mobiles. It was widely flouted and phones were confiscated. Parents had to go to the school and sign a paper stating they had read and accepted the phone policy before the phone could be returned. This was a huge pain in the ass, needless to say, and the phones continued to be brought to school.
There was a good reason to bring phones to school - parents liked to check whether their students were home after school, students liked to contact parents if a sport practice or rehearsal was canceled, etc. Parents liked phones. The school feared students would buy or sell narcotics if they were allowed to have phones. The policy generated so much opposition that a group was able to present their case for a rule change at a school board meeting. The rule was changed.
If flip flops were confiscated and parents had to come to the school to sign them out, I am certain there would be the same outcome as the phone controversy.
Some rules are based on assumptions that don't stand up to scrutiny, and some consequences are out of proportion to the crimes.
Luckily, people here tend to be practical - the deans and their secretaries were fed up with the confiscation policy too, the time it took up and the paperwork we're ridiculous and impinged on other functions of the office - and also flexible and responsive.
Even the RC elementary school my DCs attended to age 13 changed its footwear rule after a body of parents got together to complain about the previous dress shoes requirement. For about the last 20 years, students have been allowed to wear white, black, beige or blue sneakers to school. There was no issue with casual, comfortable footwear starting some sort of rot in standards. Another change that was instituted about the same time was that students up to 1st grade could wear PE clothes on PE days. This cut down on time spent changing before and after PE and also drastically cut the complaints about lost uniform items.
The social services in the high school are paid for out of the high school budget. The providers are employees of the school.