I think that's probably the most likely outcome, that we will indeed see a chill effect. Psychologists especially are, in their way, a relatively conservative group. People will say “Uh-oh”, if there's a lot of trouble. If there's a lot of activist language about it, a lot of political angling going on, many practitioners will simply resolve not to become involved. They will say, “I'm not expert enough to really make this an issue” and will just shy away from seeing any of these clients.
We will end up with clinicians, exactly as you put it, with a chill effect, simply unwilling to deal with this kind of issue; the service will become unavailable. Without a clear indication of what counts as an “exploration” and exactly what that means, anybody would have trouble going into this with the kind of confidence that a clinician needs in order to help their client.
To say that we're exploring or that a client is exploring their gender identity is to assert that there exists a concrete gender identity and we merely need to shut up and observe. There's no evidence for that for gender identity. We have evidence for that for sexual orientation, but we cannot treat gender identity as if it's the same thing.