(I've edited this comment over and over like a dozen times now, so sorry for any confusion.)

Could you please elaborate on your point? As stated, I don't see the contradiction between human thought being deterministic, and human thought being capable of deciding which claims to believe.

In your example, I would say that, even though both positions are determined by "invincible cause-effect chains", there's no rule that says both chains have to produce correct beliefs. In fact, since the claims are contradictory, only at most one of them can be correct, which means that the "cause-effect chain" of the other one must have included some step which entailed faulty information, or faulty logic. Or the same could apply to both, if both claims happened to be incorrect in some way.

To give an example, let's say person A lies to person B. If we accept determinism, that means "invincible chains of cause-effect" led to A and B believing different things, but A still has the correct information and B doesn't. The fact that both have these really long "cause-effect chains" doesn't prevent us from pointing out that A happens to believe correct information, and that B doesn't.