Rebdoniel: Most Achronim don’t read Tosfos as Shittuf being Muttar for a Goy and no one (and I mean no one) Paskens like that Meiri. According to that Meiri even ancient Greeks and Romans (and modern Hindus) aren’t Ovdei Avodah Zarah. The Meiri is not even a Tznif Lehakel. Also, the Meiri’s definition of Notzrim as a Sun Cult claiming to descend from Nevuchadnezzar (which actually existed in Provence from the tenth-15th centuries) is clearly not what the Gemara meant. And that Rosh was not even brought down as an opinion in Shulchan Aruch, if I recall correctly, so it’s hard to Pasken by it. Your quoting about Ovdei Avodah Zarah B’CHU”L is good, but R’ Moshe already pointed out (and this has to be P’shat) that that clearly doesn’t apply to those who are obviously Addukim Bo, such as the ministers, priests, missionaries, etc.
Naysberg: They believe in 1 G-d. Not a trinity. They are Avodah Zarah just as much as Islam is. And while the Ran (and, L’pele, the Tzitz Eliezer brings this down) Paskens that Islam is not Avodah Zarah, the Olam has been Tofes like the Rambam that Islam is Muttar for Goyim and for Jews to enter their mosques if necessary.
No, the reason it was Muttar B’sha’as Had’chak for R’ Sacks to attend the wedding was due to it not being Avodah Zarah, and not for any other reason.