Can the Rabbi give an example of what would be permitted?
For example, the New Testament?

I don’t think the New Testament is a ritual object that is forbidden for benefit. As for permission to read it, several halakhic decisors wrote that it is permitted for the sake of study (history, for example).

Don’t forget Tosafot on Sanhedrin 63b, that a gentile is not commanded not to believe in the doctrine of the Trinity, and therefore from our perspective there is also no issue of “do not place a stumbling block” in that regard; only for us could there be some problem of a trace of idolatry.
Though Maimonides does not hold that way.

It’s not so simple. Factually, the Trinity is a false belief, regardless of whether there is a prohibition against holding it. So there is plenty of room for the claim that this involves “do not place a stumbling block.” Beyond that, here we are talking about a book in the possession of a Jew, not a gentile.

Is there such a thing as compelling observance of the commandments by an individual? The Ketzot writes that the whole authority of a religious court to compel observance of the commandments is based on their acting as agents.

Plainly speaking, yes. See Ketzot HaChoshen, Netivot HaMishpat, and Meshovev in Choshen Mishpat sec. 3.

So if a book that might be the item most connected to heresy is not considered idolatry, what is considered idolatry? And I’d also be glad to know: does compelling observance of the commandments apply specifically to a religious court? Or can even a private individual compel observance of the commandments? Because if so, we’re in a bit of trouble with Sabbath desecrators and other transgressors…

Sorry, I didn’t see that you answered the last question.

Something that is actually used in worship.
Even if a private individual can compel, compulsion is not applicable today (you do not compel someone who does not believe, and in our society there is no practical ability to compel even someone who does believe), so there is no problem at all. By the way, even if this is a rule specifically for a religious court, you could still ask why we do not compel today.

I’d be glad to know the source that if something is forbidden for benefit, I can compel in that case; whereas if it is something that might involve the prohibition of “do not stray after your heart and your eyes,” or the other prohibitions and distancing measures mentioned in tractate Avodah Zarah and in tractate Shabbat in the chapter “All Sacred Writings,” I cannot.
Thank you.

Changing the subject but on a related theme —
(apologies in advance if I’m bothering your honor with trivialities) according to Jewish law, is it permitted to pick fruit from a field during the Sabbatical year even if the field owner does not observe shemitta?

Yisrael,
In principle, one may compel regarding any prohibition. There is no difference between something forbidden for benefit and any other prohibition. The question is whether the prohibition is agreed upon and clear, and whether compulsion is applicable in our times.

Yechiel,
How is that connected to this?
Produce that was guarded or worked during the Sabbatical year was, according to most opinions, not prohibited, and therefore as a matter of Jewish law the very fact that the field was worked improperly does not prohibit the fruit. However, if the field owner did not declare his produce ownerless, it is not clear whether from a monetary standpoint it is in fact ownerless. There is a dispute whether the Torah itself rendered it ownerless, or whether there is merely a commandment upon us to render it ownerless (Mabit and the Chazon Ish versus the Beit Yosef). Since these are monetary laws, in my opinion one should be stringent, because the burden of proof rests on the one seeking to take from another.

Would a Christian prayer book be a good example?
Like one I saw someone praying from — Daily Prayer Book.

It seems to me that definitely yes.

Assuming, of course, that Christianity is idolatry.