This has little to do with religion and more to do with power. There are secular regimes that have done equivalent (or worse).

Is it the religion itself though, or is it about tying the law execution and religion?

It's easy to check, remove religion and see if it helps or not.

It's of no use anyway. In most recent cases where one side was religious and other one wasn't, religious ones were usually bad guys. Stance on abortions, ID, this abomination. I can't remember them ever backing something good against secular people trying to do something bad.

In the spirit of fairness - really?

Communist Germany, USSR, Communist China/Mao, North Korea, Mussolini's Italy, etc.? All of those were or are "religious" governments?

I don't remember catholic church standing loudly against Mussolini or Hitler, neither russian orthodox church standing against Stalin. They were too busy fearing for their lives.