If Mineta and the Earbud girl (I've forgotten her name) can enter Yuuei with their quirks, his mobility quirk could've made it in if he'd trained properly.
Well.. Mineta is a weird fluke that should have failed purely on his personality and physique. Earbud girl on the other hand has a quirk with both solid detection abilities and close combat applications.

As for minor super hero schools. We have not been told or shown of any. And i cant think the entry requirements would be to much lower.

I see it a little like how special forces also need to set some rather tough demands for endurance and strenght. Because thats whats needed for the task they face.
Its simular with super heroes. They need to be able to deal with someone that has a strong quirk and are going on a rampage.