Well the game was made in Japan and the culture is based on Japanese culture and in Japan you have outdoor shoes and indoor shoes. And those look like indoor shoes.
It’s a Japanese game, they don’t wear outdoor shoes indoors to keep tracked in mess down. It’s his place so he wears slippers instead on indoor shoes they have for schools and offices and such.
You got to realize, that’s his lab, and at your lab, you do whatever you feel like doing.