As far as participation goes, something fun my teacher mentor did to motivate students to bring proper footwear was the Big Shoe award.
If an entire class (Say, Mrs. Higginbottom's class) wore appropriate footwear for PE, they would get a sticker placed on a board that tracked the month's progress. At the end of the month, the class with the most stickers got to take a picture with a GIANT basketball shoe. It was comical how big the thing was compared to the kiddos, haha. They got a kick out of it.
She did this for each grade level and their pictures would be displayed right by the doors to the gym.