The IRA is a perfect analogy. If the logic that calls ISIS Saudi is correct, then it's similarly valid to call the IRA a British creation.

If you are unfamiliar with the reducto ad absurdum argument, you can familiarize yourself with it here: https://en.wikipedia.org/wiki/Reductio_ad_absurdum

At the moment ISIS does promote regime change in Saudi Arabia, so the regime there really don't like them related to that, but the former history is very different.

Yes, and similarly if the IRA jailed rapists and allowed Christianity in territory they controlled, I doubt the UK would object much to that.

The fact that two European groups have cultural similarities doesn't mean that one sponsors the other. The same is true for two middle eastern groups.

Fundamentally, I bring up the IRA because I'm trying to explain by analogy to something more familiar. You seem to be viewing all middle eastern organizations as being somehow monolithic and identical simply because they are more similar to each other than they are to the west. But that's simply a fallacy.