my confidence about Turing Tests would also decrease enormously.
Why that, and not your confidence about GLUTs ?

Of course my confidence about GLUTs would also decrease enormously in this scenario... sorry if that wasn't clear.

More generally, my point here is that a conversation-having GLUT would not alter my confidence in all propositions equally, but rather would alter my confidence in propositions to a degree proportional to their relation to conversation-having GLUTs, and "I can usefully infer attributes of a system by conversing with it" (P1) is far more closely related to conversation-having GLUTs than "I'm wearing socks" (P2).

If your point is that my confidence in P2 should nevertheless be significant, even if much less than P1... well, maybe. Offhand, I'm not sure my brain is capable of spanning a broad enough span of orders-of-magnitude of confidence-shift to be able to consistently represent the updates of both P1 and P2, but I'm not confident either way.