My response (which will never see the light of day over there, because most of the "orthosphereans" are cowards who cannot stand up to *any* criticism ) --
I refuse to call them 'Muslims' because that's what the Kool Kids insist we must say (*). I grew up calling them 'Moslems', while being aware of and understanding 'Mohammedan'.
Moreover, it is *claimed* that 'Moslem', when prononced as we English-speakers pronounce the word, is an insult to the precious-and-delicate sensibilities of the Muzzies (albeit the truth).
For instance, according to this page on History News Network:
According to the Center for Nonproliferation Studies,"Moslem and Muslim are basically two different spellings for the same word." But the seemingly arbitrary choice of spellings is a sensitive subject for many followers of Islam. Whereas for most English speakers, the two words are synonymous in meaning, the Arabic roots of the two words are very different. A Muslim in Arabic means"one who gives himself to God," and is by definition, someone who adheres to Islam. By contrast, a Moslem in Arabic means"one who is evil and unjust" when the word is pronounced, as it is in English, Mozlem with a z.So, I'm all for calling them either 'Moslems' or 'Mohammedans' (or, for that matter, 'Muzzies').
But, getting back to the argument of the OP; it sounds persuasive, but does it hold up in other situations? Does it even hold up internally?
Other situations --
Suppose there is some tribe which call themselves, as many peoples do, a term that in their language means "The Human Beings", implying that they *alone* are real human beings. And suppose that there is another tribe, historical mortal enemies to the former, who call the former a term that in *latter's* language means "Shit-Eating Snakes". And now suppose that we English-speakers make contact first with the second tribe and from them learn of the first tribe ... and learn-and-adapt the second tribe's name for the first. Now, further suppose that fifty years later, our leftist Special Juicebox Wankers are having continual snits because we always refer to the first tribe as "Shit-Eating Snakes" rather than as "The Human Beings". What is a sane and moral man to do? Nothing! We are speaking English, and in English the second tribe's name for the first tribe is just a noise with no inherent meaning; that is, we are *not* calling them "Shit-Eating Snakes". Moreover, *refusing* to bow to the demands of leftist Special Juicebox Wankers is a moral good in itself.
The point bring that in English 'Islam' does not mean "Submission to God", and 'Moslem/Muslim' does not mean "One who submits to God". In English, those sounds merely signify a particular social-political-religious ideology and its adherents.
So, the reason for us English speakers to refuse to call them 'Muslims', rather tham 'Moslems' or 'Mohammedans', is not because doing so implies that their religion is The One True Religion, but rather because they, and our internal enemies (i.e. the leftists), insist that me must.
Internally --
The OP's argument depends upon the premise that 'Allah' *is* God, and thus that 'Mohammedans' *are* "monotheists" (**). I reject the premise and its implication.
(*) In similar wise to how when they refer to a Mexican by name, they pretend suddenly to have morphed into a Castillian.
(**) For that matter, I object to being called a "monotheist", as though Christianity (and Judaism) were on the same continuum as classical Greco-Roman paganism or present-day Hindu paganism.
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Edit:
Here is another point in favor of calling them 'Mohammedans' -- Mohammad looms larger in the daily life of not-even-particularly-devout Moslems than Christ does in the daily life of even the most saintly-and-devout Christian.
Consider --
If a saintly-and-devout Christian announced that she (*) were going to make it her life's work to determine how Christ took his bowel movements, so that all saintly-and-devout Christians may do likewise, what would the rest of us say to her (*)? We'd say, "You aren't saintly-and-devout, you're insane!"
But, to the 'Mohammedans', it is a very important matter -- sometimes even a life-and-death question -- to know how Mohammad took his bowel movements, and to do likewise.
(*) I am, of course, mocking those fools who, vainly imagining it is even possible to appease the Kool Kids, deliberately use 'she' when English demands 'he'.