No, this makes total sense to me, and I feel you about godding. Baze is a hugger, too, and the way I'm planning to deal with it is to have him just open his arms in the offer of a hug, and then then the other mun can decide. I've been blessed with Ibani mun and Chirrut mun who basically let Baze hug their pups anytime, so he gets most of his physical contact needs fulfilled that way.

TL;DR: Barry can hug Baze anytime he likes!