I have been teaching basic English (numbers, colours, names of animals) at many Japanese nurseries. At all of them, visitors have to remvoe their shoes. Slippers are always provided.
It is a great idea. Nurseries need to be hygienic places for children, and having a no-outdoor shoes rule must help a lot. I once worked as an administrative assistent at a nursery and it was not always as clean as might be desired.