I really thought therapists were some other kind of species.

But T's are adults. They should make their rules/boundaries that work for them. If a T offers to a client that she/he can contact T during their break, then that client is allowed to contact that T. If a T wants nothing to do with work during their break/vacation, then T should not offer it. It's best for a T to have a seperate email for work only.
My T's have a work email. They probably only look at it during their workhours. I know that T1 does that. Not totally sure about current T, but I know she doesn't do email during her vacation.

I can send them an email during their breaks, but I know I won't get a responds until they're back at work. And I'm allowed not to like that.