Earlier quoted context omitted.
There's no such thing as "obviously a shill"—I can tell you from years of experience that the vast majority of such accusations crumble instantly on investigation. Commenters are far too quick to hurl them at other commenters. There seems to be a cognitive bias where one's feeling of good faith decreases as the distance between someone else's opinion and one's own increases [1]. If so, then everyone has a "shill thre…
A shill is anyone who lends credibility to a con (or more modernly, PR) by claiming to believe it themselves. This can be witting or unwitting, but if what you're doing is repeating PR, even if its because you believe it, you're a shill. In fact, a grifter prefers their shills to be defending them in good faith. The basic currency of a con is confidence. This is easier to wield if you don't have to pretend. Unfortuna…
The mistake in your argument is to assume that accusing them will reduce their influence. Just the opposite is true: it will amplify their views and stiffen their errors, and they will push back twice as hard and twice as much. Maybe their argument quality won't spike, but their energy level will.
Worse, if you're right, accusing them will discredit the truth and reduce your influence. Undecided readers will look at the thread, see you being aggressive, and instinctively side with the other.
It also poisons the forum, because when people feel unjustly accused, they take it as license to lash back twice as hard. "But they started it" is a deeply felt, maybe even hard-wired, justification for escalation. (I bet there are primate experiments demonstrating this.)
Therefore, accusing people or denouncing them as "repeating the lies of $BigCo" (or $Party or $Country in political arguments) is just what you should not do—there's no upside, beyond the momentary feeling of relief that comes after blasting someone. If you want to correct errors and combat lies, you need to provide correct information and good arguments in a way that the other person is more likely to hear. As a bonus, that will help you persuade the silent audience too.
The effects of PR and propaganda in getting people to hold false views is enormous, but I don't think it's possible to separate out from other reasons why people hold false views in good faith. It's much too big, and those influences are raining down on all of us from all angles.
How to dissuade someone of false beliefs is a pragmatic question. If you tell them "you've been deluded by propaganda", it will only land as a personal attack. Better persuade them that they've been working with incorrect information, and let them draw their own conclusions about the propaganda side of things. The latter medicine cannot be spoon-fed into someone else's mouth—one has to take it oneself.
[1] (Your usage of the word shill is different from the dictionary definition (https://en.wiktionary.org/wiki/shill) and the etymology (https://www.etymonline.com/search?q=shill). Terminological differences make discussions slippery, but I'll respond to what I think you're saying.)