ooh can I play
“Isn’t it proper to first ask the question whether Yidden ought to be celebrating a wedding “anniversary” altogether?”
Not really. Like everything else it is muttar unless it is assur. So come up with a reason to asser. And I’l gladly explain why you are mistaken.
“And, secondly, are you celebrating based on the Christian calendar or based on the Jewish calendar?”
Probably neither. Though it in all likelihood may be based on the solar/civil calendar. It would hardly be the first thing based on the solar calendar. Vesein tal umatar, birchas hachama, nittel (if that is your minhag) Are all based on the civil calendar. For that matter the entire structure of our leap years is designed to keep us in sync with the solar/civil(/christian?) calendar so that every 19 years Jewish and secular/solar/(christian?) dates coincide give or take up to 2 days.
Furthermore As you may know the Gemara at the end of Makos says that “hasatan+ = 364 kineged the 364 days a year the satan has power except Yom kippur. Guess what kind of year has 365 days?
bottom line is while the phrase stam “a year” is counted based on months (i.e 12 or 13 lunar cycles), this is only becasue of a limud hakasuv of chadshim atah moneh and not days. If not for this limud “a year” would in fact be counted based on days i.e. the solar year which you call the “christian year” regarding a neder, sale, yahrtzeit etc There is no such limud regarding anniversaries, thus there is nothing wrong with counting based on the solar/civil year.