My kids have been to two different types of school in the US, a RC elementary and a public (state) high school.
I don't remember any untoward fussing about anything in either school even though the elementary school had a uniform.
There was a list of school supplies every year for the elementary school that was every bit as specific as the French list posted upthread. Every year, the list had at least twenty two items, with sizes and preferred brands. However, you could get away with using last year's markers, highlighters, rulers, folders, crayons, paints, protractors, etc. We also had to supply items like antibac wipes, paper towels, boxes of tissues, ziploc bags.
The only thing (and it really only became a Thing from about 1998 on) was hydration. Water bottles were de rigeur beginning about the start of the century.