>>> the Church has affirmed that Muslims and Christians worship the same God. Jews, too.
Not correct. Muslims directly reject Christ as being God, while attempting to say Christ was a prophet.
By their own koran rules, they must reject prophet status because Christ actually said he was God - that is the law that was used to sentenced Him to death, for blasphemy. Ie. Muslims say he lied - a prophet can never utter even one lie. So do many Jews, reject Christ, they have rejected even their own (Torah, etc) prophesies of a 'coming Messiah' - much less a prophesy that has already occurred.
The last few popes *and many of the hundreds of years of the roman catholic church* HAVE stated, quite publicly and as 'edict' that Muslims and Christians do worship the 'same god'.
THOSE POPES ARE APOSTATE, without faith. They have denied Christ.
Martin Luther posited that the papacy *ie. the office of the pope* was the actual capital A Antichrist.
Mormons also do not worship the same 'god' - since they are polytheists - believing that everyone (good enough sic.) can become god.

Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good ...