Quite commonly one selects one's belief on a totally inadequate basis (affect heuristics, political sympathies) and then reinforces this belief by arguments constructed with the belief in mind. This is what the post was warning against.

That's an application of the post's argument, true. But as gRR notes, the literal meaning of the post discusses how we judge information presented to us by other people, which we receive complete with arguments and conclusions.

Once an argument is given in favor of a belief, and that argument has no logical faults, we must update our beliefs accordingly. We don't have a choice to ignore a valid argument, if we are Bayesians. Even if the argument was deliberately built by someone trying to convince us, who is prone to biases, etc.

Yes, filtered evidence can in the extreme convince us of anything. Someone who controls all our incoming (true) information, and can filter but not modify it, can sometimes influence us to give believe anything they want. But the answer is not to discard information selected by non-objective partisans of beliefs. That would make us discard almost all information we receive at second hand. Instead, the answer is to try and collect information from partisans of different conflicting ideas, and to do confirmations ourselves or via trusted associates.

Eliezers's followup post discusses this.