I strongly suspect that the most obvious explanation is indeed the correct one.
That being that the Qur'an and Islaam are enthusiastic proponents of peer pressure and other forms of compulsion for the adoption of Islaam, but at the same time reject nearly all of the responsibility for that trait.
The statement exists in direct defiance of the reality of the doctrine itself. That is not an oversight, but a deliberate attempt at obfuscation for ideological purposes, a statement of values, emphasis and goals, an invitation to take a certain bias and be an accomplice in the price that sustains that bias.
In short, it is an hypocritical lie, stated at just the right moment to confuse criticism of Islaam and further the goals of proselitism by attempting to ease to conscience of dutiful acolytes as they deal with the reality that not everyone can ever be a Muslim.
The verse makes two clashing statements and expects the reader to provide the willingness to accept them as fitting besides each other. It is reminiscent of Andersen's tale of the Emperor's New Clothes.
The Emperor's New Clothes - Wikipedia
That contradictory verse is useful for the purposes of artificially increasing the lasting power of Islaamic doctrine, because the very insistence on treating the contradiction as somehow unremarkable or even non-existent confuses the thought processes and expectations of Muslims and apologists. The habit of reading the verse and stopping consistently short of pointing out the contradiction is a constant invitation for Muslims to provide their own (unavoidably convoluted) explanations for why other people seem not to perceive it, while also creating the expectation that any critics should be polite enough to restrain their voices and assume that there is somehow an explanation that just happens not to have been stated or well understood at that moment.
In that sense it is quite a prodigy of skill, a very efficient and resilient marvel of manipulative doctrine. Had this specific verse not been in the Qur'an, Islaam would have a considerably harder time expanding and defending its own reputation, but it would also be more honest with itself and create a lesser percentage of disappointed former adherents that end up rejecting not only Islaam, but also religion and even theism. Muslims and former Muslims tend to confuse the three concepts, because the Qur'an teaches them to.
It is also a rather unique verse by Quranic standards, so much so that it is very predictably recalled whenever people are reminded of how Islaam expects compulsion; nowhere else in the Qur'an there is any clear attempt at denying that expectation, so that necessary role falls entirely to this purposefully flawed verse.
We should not neglect to notice that the verse attempts to present "religion" as synonimous with Islaam, characterized there by the belief in the existence of Allah and the adoption of the marvelously ambiguous and manipulative Islaamic rejection of "idolatry", that unholy blend of literal worship of idols with worship of "evil", Shaitan/Satan, or just adoption of deities that happen not to be the Quranic Allah.
Symptomatically, the translations of that what is to be rejected are all over the place. It may be "evil", "false deities", "Shaitan/Satan" and/or "belief in idols". Islaam is so bad at distinguishing between those very different concepts that one has to conclude that the doctrine wants to present them all as one and the same thing.
Al-Baqara 256 - Wikipedia
Naturally enough, Al-Baqara 256 is widely understood not to be one of the abrogated verses. That means that we can't use less contradictory, more rational statements of the Qur'an itself to clarify this one, despite a very blatant need to make the attempt.
