Go look up this Tosfos that allegedly says Xianity is not AZ; you will find that it doesn’t quite say that. At most it’s one option given, and not the final one. The basic position of the Baalei Hatosfos is that it is AZ, but that for one reason or another we’re allowed to do business with them, and to derive benefit from buying and selling their wines, despite this fact.
All this discussion though is beside the point: rather than explain why going to churches is really muttar, etc., let’s accept what seems pretty clear, that it is assur. <i>However</i> there is a whole area of halacha for shtadlanim, which has very generous heterim. Nor is this some modern mishguas; it goes back all the way to Nechemiah, who was called Hatirshoso because he received a heter to drink goyishe wine! Have you heard of such a thing?! Imagine anyone today daring to drink goyishe wine becuase he’s a shtadlan! And yet Nechemiah did so, and he did it with the permission of the chachomim of his day. Because shtadlonus has its own gedorim and one can’t learn from that to other things.