I would not eat with a therapist. But I usually throw up before going or am very anxious while there. Even if I did not have that sort of reaction to the therapist, I still would not eat while trying to talk to the woman.
The only reason I can think of to eat at an appointment is if the client has to rush back to work or something. Otherwise, if it were me, I would simply eat after. I don't find, for me, it matters much if I eat at noon or 1 or 1:30 or whenever. It might matter if I were taking some sort of medication or had diabetes or something like that. I would not eat at an appointment with my accountant or other professional meeting either.
When the therapist eats is not my problem.