I don't know why someone would become (or continue to be) a therapist if they are not comfortable with clients exhibiting obsessive behavior, especially given that the structure of therapy provokes this kind of response with regularity. If a therapist has stalker fears, they ought to see their own therapist about that, so it's not clouding their judgement. Or find another line of work. I don't think this is unreasonable.

The only expectation I see here is that therapists not rush to judgement or pathologize the client's behavior (as people seem to be doing in this thread), whether due to their own fears or ignorance.

By virtue of payment, clients have earned the right to get the benefit of the doubt, within reason. Therapists are held to a higher standard because that is their job.