Well, and there are a hell of a lot of Catholics pushing for these kind of modern reforms, too. You're not going to get American Catholics to decide, as a group, that birth control is a bad thing; it's just not going to happen. The push for women in the clergy is only going to get bigger. And while gay rights is still a flashpoint for now, public opinion has only ever moved in one direction on the subject. The Church's views on abortion are pretty entrenched, and it's still a divisive issue among the mainstream public in much of the developed world, but over time I expect that'll change too.
One of my best friends from high school came out of the closet shortly after starting college. Not long after, his parents quit the Roman Catholic Church. They're devout and were very active in the church (and legitimately wonderful people, I might add); they joined a more progressive offshoot sect that (1) does not think their son is condemned to hellfire and (2) allows Mom to be a preacher.
Leastways, that's how I heard the story secondhand; I'll admit I haven't been in great touch with my friend over the past few years so there could be a bit of Telephone at work here.
But I think there are lots of people like that. Sure, there's an entrenched power structure that's resistant to change, and a pretty huge reactionary faction among the faithful that doesn't want to see the church change its views on what they consider to be core values and principles. I think Francis is doing a pretty good job of speaking to those people -- "Hey, you want core principles? Be humble and help the poor; all that other stuff is less important."
And there are plenty of people like my friend's parents -- people who are deeply religious, who consider their Catholic faith to be a fundamental part of their identity, but who will walk away and find some other place to worship if the church continues to condemn their friends and families.