It is indeed a false dichotomy that presupposes that the Church must change to accommodate and accept anyone and everyone, regardless of their immoral lifestyle. It is those who want to be part of the Church who must change, and not vice versa.
Those who hold out in false hope that the Catholic Church will ever condone same sex “marriage” or abandon the fight against it are doomed to lasting disappointment. It doesn’t matter if 99% of lay Catholics are deluded into thinking that same sex “marriage” is not an evil. Our current pope, long may he reign, consistently appoints new bishops and archbishops who staunchly defend holy matrimony, and he will continue to do so. The next pope, and those after him, will also defend the sanctity of marriage in every way possible. Anyone who can’t see that plainly, and thinks that the Vatican will somehow be swayed by popular opinion on same sex “marriage” doesn’t understand the Magisterium, papal succession or the inexorable force of Church teaching and tradition.