The history of that region taught the Chinese government that if they don't do something about it, then extreme religious groups may cause serious damage.

The presence of the "nonviolent" but complacent and complicit minority in these countries is what enables things to be the way they are. Maybe not everyone participates, but if you poll them on whether or not they support honor killings, oppression of women, etc. a large number will agree. This is not some fringe set of beliefs. Now personally I don't think we need to "do something about it", but the U.S. has actually gone out of it's way to create chaos in the Middle East and empower fundamentalism. We treat Saudi Arabia as an ally while they export poisonous propaganda, we help remove mostly secular dictators from power (who are generally opposed to Islamism and who keep the peace between ethnic groups), and chaos, terrorism, and explicitly Islamist governments with far more extreme policies is the result. Basically, if we really wanted to "do something about it" we'd just stop doing what we've been doing for decades. And yes, that includes not overthrowing Assad. The same people claiming he gassed his people are the same ones that said Iraq had weapons of mass destruction. I don't buy it.

As opposed to the western approach which lets religious fundamentalists profess their anti-semitism, anti-atheism and misoginy freely and violently?

Example: http://www.france24.com/en/20180511-saudi-financed-belgian-m...

And while freedom of expression is important, it is limited (especially in Germany). Racists expressions are a no-no pretty much everywhere.

Now Jews feel increasingly unsafe in the streets of Europe.