More power to you.
Rabbi Melamed made a calculation of what percentage of the pamphlet is words of Torah and what percentage is mundane material. And that was part of his ruling.
My question: a certain rabbi writes a long article saying that in his opinion one should act this way or that way, and derives it from the weekly Torah portion or from books of Jewish law.
But sometimes an honest person can see that he is mistaken and misleading others, and what he proposes is the opposite of Jewish law, the opposite of decency, the opposite of logic. The opposite of Torah. The opposite of God's will…
Simply warped in a terribly crooked way.
Does such an article count, percentage-wise, as words of Torah or as mundane material?
And I am asking about clear-cut cases, not borderline ones. And multiply that by 30-40 pamphlets lying around in the prayer hall, study rooms, women's sections, etc.—altogether it's not a small amount of money that they demand in the blue bin…
We would be happy to hear the honorable rabbi's answer.

That has nothing to do with the question of whether you think these things are correct or not. This is a Torah discussion.

More power to you.
My question: are there any boundaries for when this is just a private opinion [not decent, not just, not upright, certainly not Torah], or does anything written by someone who has the title "rabbi" count as words of Torah?
And what if the writer is not ordained as a rabbi, but he has a PhD in the Hebrew Bible, Oral Torah, or Jewish thought, or not a PhD but is knowledgeable in the field, such as a teacher of those subjects—will whatever he writes also automatically be included as words of Torah? Are there any boundaries that the rabbi agrees are outside the percentage count of words of Torah, and count as mundane material? Or just an article / interpretation / political preaching? [I may be insisting a bit, but in my humble opinion a significant portion of the articles in some of the pamphlets belongs in the borderline category.]

If you want to say that they write a lot of nonsense there, I completely agree. If you want to say that they use the pamphlets to push political agendas, I also agree.
Beyond that, in my opinion a discussion in Jewish thought or aggadic literature is not Torah in the concrete sense, and therefore does not require genizah, even according to the views that analytical Torah study does require genizah.
Still, someone who conducts a halakhic discussion and presents his view—that is Torah, even if he is mistaken. If it isn't Torah and he merely presents it that way, then it isn't.
I do not have a more specific definition of that boundary, and I don't think such a definition can be offered. If you want to raise an example and discuss it, we can. Otherwise, I'm done.

With God's help, 2 Ziv 5781

Regarding Rabbi Melamed's distinction between 'mostly words of Torah' and 'a minority'—the Minchat Yitzchak compares newspapers to letters in which verses are written as a stylistic flourish, which have no sanctity, and likewise newspapers intended for news in which words of Torah are mentioned incidentally, since they were not written in order to study from them.

It would therefore seem that when a newspaper has a special section for words of Torah, and especially when the newspaper is published by God-fearing people whose intent in that section is certainly that people engage with them as words of Torah—then that section, which was printed for the sake of words of Torah, has sanctity and requires genizah.

So too Minchat Yitzchak brings (sec. 18, or 20) in the name of the book Yerushat Pleitah (sec. 29): 'All this is when they were written for mundane purposes. But many times newspapers print … also sermons and words of aggadah and sayings of the sages and laws and the like, and all the more so in newspapers of the God-fearing, whose intent is to teach ethics and fear of Heaven from them—then they certainly have the status of sacred writings, even if they were written in the vernacular.'

Minchat Yitzchak also cites the responsa Zeken Aharon (part 2, sec. 70), that even if after the fact we are lenient and say that once printed they do not require genizah—still, what permission is there to print words of Torah that will come to be lost and disgraced?

It would be fitting for the publishers of the pamphlets to do as some Haredi newspapers do, marking the individual pages that require genizah, so that the reader can quickly and easily identify the pages that contain words of Torah.

With blessings,
Yaron Fishel Ordner

By the way, the very bringing of these pamphlets into the synagogue is a stumbling block, since people fail by reading them during prayer and the Torah reading. Rabbi Ehud Krakover instituted a nice practice in Kokhav HaShahar: they made a stand for the pamphlets ליד the grocery store, and whoever wants takes them home from there, and they do not enter the synagogue at all.