A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.
No, you can't deny women their basic rights and pretend it's about your 'religious freedom'. If you don't like birth control, don't use it. Religious freedom doesn't mean you can force others to live by your own beliefs.
What we should grasp, however, from the lessons of European history is that, first, there is nothing necessarily benevolent about programmes of European integration; second, the desire to achieve grand utopian plans often poses a grave threat to freedom; and third, European unity has been tried before, and the outcome was far from happy.