I agree that the therapist ought to ask the patient if it's okay for the dog to be there. Many people are allergic to dander. Many find them distracting, or just aren't comfortable around them for whatever reasons. (My T asked on the first visit. I really appreciated that.)

That said, it's not analogous to e-cigs. Dog dander is a known quantity. Secondhand e-cig smoke is not. It's not scaremongering to be concerned about it, and it's not an overreaction to ban e-cig use indoors, as many businesses and local gov'ts have done. If future research demonstrates that the smoke is harmless, great. Until that day it's entirely reasonable to be concerned about those things.

I say this as a former smoker who feels no urge to wage holy war against tobacco. I'm convinced nicotine attenuated my depression for many years. If it had no health consequences I'd still be chewing gum and wearing patches.

'Increased levels of toxic metals' in e-cigarette secondhand smoke Medical News Today