School wants 3 years old to wear regular underwear?

My son is 32 months old now, but by the time school starts in fall he will be 3 years old. I have applied in couple of good schools in my area. Their condition is that child has to fully potty trained and come in regular underwear, not in pull ups. My son is 95% tells me when he has to go toilet but sometime he gets busy playing so wet his pull ups. But poo poo, he hasn’t done in pull ups from past 3–4 months. But right now he doesn’t know how to clean his bottom and put on the underwear or pant properly. He might be able to do by the time he will be three. I really want him to attend one of those schools, because I find them really good for my son. But only this is worrying me, if he would be able to dress himself fully or not have any accidents by the age of 3? Please suggest.