I will have to think on this a bit more. But my first thought is that a will to violence in any direct sort of way is not required.
For example, many people in the US who call themselves fundamentalists think it's perfectly OK for a teacher at a public school to get up in front of everyone and tell them all about God, as long as it's the right God. And that this is especially important if some of the children in the class have parents who don't think that the right God exists.
Yet they wouldn't choose to start a new inquisition. As long as the violence is quiet and hidden behind the soft club of the state, it's OK.
OTOH, secularists do the same thing by insisting that people with strong religious beliefs pay for a school system that doesn't teach their children the values they hold dear. A practice I think is similarly evil. I would call people who think this secular fundamentalists.
And there's the Amish, who I have no disagreements with at all, who might definitely be called fundamentalists by your definition. Nobody does though.