I want to discuss this topic via a different angle now, that of an analogy to rape and what it means to "consent", but for now I can only issue promissory notes that the dots will be connected.
Suppose there was a woman who wanted to charge a man for rape on the following grounds: the man told her that he was a rich tycoon, but it turned out that he was a pauper. Thus, goes her argument, she only consented to have sex with a rich tycoon, she did not consent to have sex with a poor man, thus, she was "forced" into non-consensual sex, ergo she was raped.
Prima facie, we think this is an absurd charge, just because she was mistaken as to certain features or aspects of the identity of her sex partner it does not follow that she did not consent to have sex with him. The referent of the pronoun "him", and the identity of the same, is sufficiently determined by the empirical appearance and physical presence of the man, she consented to have sex with this man who is physically present at the encounter, regardless of whatever else she believed about his life history or personality, etc.
Let's test this new criteria by looking at another example. Suppose a woman was married to a man who has an evil identical twin. The evil identical twin decides to sleeps with her, so, when the husband was out, he comes back home under false pretenses of being her husband. She consents to sleeping with the physical person before her, notwithstanding that it isn't her husband. Later, the deception is discovered, the question here is, was she raped?
Does the fact that, in the wife's mind, she did not consent to sleep with the evil twin, override the fact that she also consented to sleep with the physical person before her? Which fact should prevail here?
So we have here two conflicting intuitions:
(1) In the first case, you did consent to have sex with X, notwithstanding you being mistaken as to who X is, e.g. a rich tycoon, by virtue of consenting to the mere physical body before you. As long as there is an empirical causal connection between the physical body and the object of your consent, you did consent.
(2) In the second case, you did not consent to have sex with X, notwithstanding the fact that you did consent to have sex with the body before you, because you are mistaken as to the identity of the person before you. Your conceptual understanding of the object of your consent determines the referent of your consent, empirical and physical causation is not enough.
The conflict as such is: which determines the intentional object, in this case, the object of consent? (1) is the empirical causal connection, (2) is the conceptual identifier.
I think this analogy is a suitable launching point for discussing what does it mean for a person to worship an entity, what determines the intentional object of worship? A sort of empirical causal connection which is not contingent upon right understanding? Or must the intentional object be determined by right understanding?
Let's frame this another way: What is the sin of the Golden Calf in Exodus 32:1-8? Was it a First Commandment violation, worshipping something else besides Yahweh? (Even though in verse 5 Aaron expressly declares "Tomorrow shall be a feast to Yahweh.”) Or was it the sin of the Second Commandment, worshipping Yahweh by means unauthorised by Him, as such a mistaken understanding of what Yahweh has willed and taught, even if the intentional object of their worship is Yahweh?
For the sake of completeness, I will rehash this common example in analytic philosophy which I've given a thousand times to explain the difference between sense and reference:
Ancient astronomers have observed what seems like two different stars which appear very differently in the sky, the Morning Star, and the Evening Star, and for some time it was believed that they were two different stars. However subsequent observation established that they in fact the same star, Venus, they merely appeared differently at different times of the day.
Now, while the terms "Morning Star" and "Evening Star" refers to the same object, i.e. Venus, they obviously do not have the same sense, they are not synonymous with one another, and no amount of semantic analysis or studying the words themselves will lead one to infer that the Morning Star refers to the same planet as the Evening Star. To establish that they refer to the same thing took astronomical observation, not philosophical speculation. Likewise, the phrases "the sum of 1 and 1" and "the definite integral of x from 0 to 2" refers to the same number, 2, but they obviously do not have the same sense, while a toddler can understand the former, secondary school calculus is needed to understand the latter.
I suggest here that this question really hangs on whether you think knowledge of God is (1) perceptual or (2) conceptual, analogous in the rape cases as to whether you think empirical causal connection/perception determines consent over conceptional understanding of the object of consent.
Romans 1:20 seems to use language for both: "For since the creation of the world His invisible attributes, both His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse."
Thus, there is the perceptual element that people can directly "see" or "perceive", "the eternal power and divine nature" from looking at "what has been made", and so it is "understood" conceptually.
If you prioritise the perceptual over conceptual, then you determine what the object of worship is by way of determining or analysing how they came to the belief in a causal-historical way, e.g. did the object of worship arise from beholding and looking at the world to "see" or discover the divine power behind and over it. Thus, whatever else they may believe about the object of their worship, which may be mistaken, the object of worship is fixed as long as it arises from the correct perception. The heathens as such would be guilty of mostly Second Commandment violations, not First Commandment violations. Although if they did identify God correctly and still worshipped other gods, that would be a First Commandment violation. If you prioritise the conceptual on the other hand, then for the object of worship to be fixed, you need to conceptually understand what you are actually worshipping. Thus, if your understanding is wrong, then the object of worship is also wrong.
It seems to me that from Acts 17:23, the main sin of the heathens is Second Commandment violations rather than First Commandment violations:
"For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you."
Thus, Paul didn't say, you are worshipping the wrong entity, or even a demon, he says merely that they are worshipping in ignorance, and he declares explicitly whom, the true identity, of Him, whom they already worship.
As such, it seems to me that to determine if an act of worship satisfies the First Commandment, it just needs to pass the Romans 1:20 test, perception of eternal power and divine nature over and from creation. Any other mistaken belief about this eternal power or divine nature would simply fall under Second Commandment violation, which the fullness of biblical revelation corrects and perfects.