"In Iran go back to people being pissed off when Islamic law was replaced with secularism by Reza Shah in the 1920’s"
I don't know the details of this but I can tell we had a similar situation when Turkish Republic was founded on modern and secular principles, which sounds great in theory but in practice it was observed as eradicating religion from public life. When you look at what was done in that era, you'll see nothing less of social engineering. Throughout its history, religious people were oppressed in a way you'd see with France's laicism. When you oppress people unnaturally, you'll get bigger reaction and motivation. If you push enough, you'll get extreme response (I guess) as in Iran.
"But I do believe they exist and they could make a different choice, for democracy, for equality but they are actively choosing religious ideology."
I agree with your previous statements that most people in any religion (or in lack of religion) want to get on with their lives. But when we use terms like "Islamic terrorism" or "Islamic extremism", then we don't give the chance to Muslims (who are mostly moderate) to distinguish themselves. Also, without acknowledging the root causes of the problem (as I stated briefly in my previous response) we can't solve the problem of extremism.
"Right now it is Islamic extremism that is harming so many people."
Again, this is the easy way out to call only one side as the extremists, especially associating it with a religion whose members are mostly moderate. Especially, when the victims of these extremists/terrorists are (moderate) Muslims. The other factors that feed this extremism are Zionism and Evangelical Christianism. The warmongers of every side are using all of these for their own power games. If we want to be fair and really want to solve the problem of extremism, we need to call out all the root causes.
Long story short, using the term "Islamic extremism" is basically victim blaming and gaslighting.