it seems like you think their understanding of God, though rational
Can we get rid of “rational” as the criterion by which we determine if someone is worshiping the true God? Rationality is great and necessary on some level, but surely every heresy started with some rational musing against what seemed/seems irrational. Nestorius thought it was irrational that a human being should give birth to God, and out of his entirely rational objection a great faith-destroying heresy was born. Arius thought that the Holy Trinity was irrational, and by his objections and artful sophistry he separated himself from the true faith and took vast swaths of the world with him. Both of these men were entirely rational – and
absolutely wrong.
is resulting in them worshiping something other than the object of their rational comprehension.
Indeed, because rationality does not guarantee correct worship. In fact, it can very easily lead away from worship of the true God. See above.
Even if reason tells them that God…
Regarding this clause (even if reason tells them…) – yes, and? No one has ever gone so wrong in following their reason as when they challenged God (the true God) to conform to their own little world and their definitions of what God can/should/can’t/shouldn’t do. When God first comes to Moses to tell him of his role in the leadership of the people, Moses gives God a perfectly
reasonable excuse: God, I am not eloquent. I’m certainly not the best person for this job. God is having none of it, of course, and so uses Moses, with all his imperfections, to be a great leader of His people. If God had cared for Moses’ very rational excuse, then perhaps it could have set a precedent by which man’s rationality can dictate to God what is right and what is true. But that’s just not what we believe in Christianity. God calls the shots, and most often what he calls us to do is exactly that thing that we can’t do (by ourselves and our reason). We don’t say “This is God (or from God); my reason has guided me so.” We believe in what reason tells us not to, because Satan deceives us by our eyes and our logic, but our faith is above all that because our GOD (the true GOD) is above all that. Reason (in the person who is living in God’s will) can lead us well, or it can (in the person who is living as a slave to something other than God) lead us to ruin. It cannot in either case be the defining factor of our FAITH.
I don’t know how we can engage with people intellectually in such a circumstance.
Not very “reasonable”, is it?

And yet here we are…
I would look at it in a different way. None of these non-Christian sources can add anything to my faith, because the Christian faith is not lacking in anything. We don’t need them, strictly speaking. But we can use others’ understandings and the writings generated by them as a springboard to bring people to the truth, and in as far as they may facilitate that they are not absolutely useless. I think I wrote basically the same thing already with regard to Islam in the first paragraph of post #77.
If someone directs their worship to these things, how does it go “astray” if they also have incorrect ideas about God, or incomplete ones? Does God reject their worship? - obviously he must perceive it.
Since I am not God, I really can’t comment on this. God may accept their worship, as He knows what they are trying to do/think that they are doing, but that is entirely up to God and I can’t say that it does happen or doesn’t. I really just don’t know. What I do know, however, is that we,
the Christian people, are held to a higher standard, because there is NO doubt that we know the true God. We embraced Him openly just as surely as others we are discussing rejected Him openly. So we cannot now let go of Him in front of others, and say that it is somehow okay that they continue in their worship while in rejection of Him. The time is coming,
and now is, when we must worship God in spirit and in truth. Only Christianity certainly has the spirit, and only Christianity has the THE TRUTH.
I am guessing you mean you do not accommodate them?
Yes, pardon me. Left out a very important word there! I do not accommodate them. Do NOT.
The question is do they have some perception of the “real” God, and are they really able to direct their worship to him? (And what do we need to do to direct our worship to God anyway? Most people pray, including I suspect Muslims, simply in hope that he hears.)
I’m not understanding the point of your question. “Do they have some perception of the real God”? Well, since they are not worshiping the true God, I don’t know what their perception has to do with anything. Is it our perception that determines who or what the true God is? The Muslims perceive that God does not beget, so God does not beget? The Jews perceive that Christ is not God, so Christ is not God? The Scientologists perceive that God is some sort of alien overlord injecting brainwashed alien souls into volcanoes, so God is some sort of alien overlord injecting brainwashed alien souls into volcanoes? But seriously, what do people’s perceptions of God have to do with anything? I believe that God is above our ability to perceive Him. The “ocean in the bucket” scenario of (if I’m remembering correctly) St. Augustine. God is the ocean. Our perceptions are the bucket. In every non-Christian religion, there’s a hole in the bucket, dear Bluegoat.