A conservative NO would be aghast if a Catholic went to pray at a ѕуηαgσgυє? I don't think so.
No, I know enough of them. They denounce the local Seder meal at their NO church, going to pray at a ѕуηαgσgυє or Orthodox church, or even SSPX ... but then do the old see no evil, hear no evil routine when it comes to the V2 papal claimants. It’s like the old The Wanderer publication which would excoriate one bishop after another for interreligious services but then ignore it when Wojtyla did the same thing or worse. If, say, an NO bishop had gotten a mark of Shiva on his forehead, they’d go ape over it, but then justify Wojtyla doing it.