Yes, it is.
>The evidence is that if you look at the big pro-life groups, they are not just anti abortion, they are also anti birth control.
That is incorrect, and a good example of the bubbles being real. You are just looking at church opposition because that's what the media likes to focus on showing. And it would not make the liberal idea of the conservative view correct even if it were true. Christians who oppose birth control do so because they value the traditions of their culture, not because they hate women. Again, most of them are women. And many of the people who are portrayed as "opposing birth control" actually just oppose having their tax money used to pay for other people's birth control, which is not the same thing.
>So it is not entirely irrational for liberals to think the way they do about this.
It isn't irrational. Being wrong is not the same as being irrational.