This stands in such stark contrast to its view as a "freedom of religion" here in the USA.
There's certainly religious and political circle overlap, though that be caused by echo chambers and social influence.
For example, why are ~50% of US men anti-abortion and only ~33% of women against abortion? Is it because men are more religious? Are 33% of women against abortion only because they are religious while 67% of women are athiests?
It's naive to think that a secular society is a unanimous one.
To give you an example, let's just consider people who support abortion: do they all agree that you should be able to abort at any point up until birth?