Sure. Except Israel has led to the formation of sizeable private armies including Palestinians and non-Palestinian arabs over time, and in relation to Saudi Arabia was a key motivator for Al Qaeda. There are people risking their lives to fight that country in every single one of Israel’s neighbours.
I think it’s safe to say the issue is more than a pet cause across the region.
You've never spent any real time in the mid-east. It shows.
Certainly Arab Muslims get upset, loud, and to western sensibilities violent over the issue of Palestine. It ranks right up there with the 150 other issues Arab Muslims protest and fight about which include, but are not limited to, court verdicts they don't like, regional religious leader edicts, things in western newspapers, particularly egregious calls in soccer, and battles from 200BCE that there are only oral histories of.*
So, Yes, there are Saudi civilians that will protest, probably this week, about Israel, this move by Trump, and the "occupation" of Jerusalem. No, recognizing the capital will not actually effect politics in the region on a timescale measured in months, much less years.
Here's the nasty, actual truth: There will be no peace between Palestinian Muslims and Israeli Jews until one or the other is wiped out Carthage style. The "owner" of Jerusalem is whomever won the last war, has been for centuries, and will continue to be for the foreseeable future. Whichever group lost the last war will use violence to try and win it back. The idea that there can actually be peace that lasts between two such diametrically opposed cultures and traditions is a particularly Western conceit, and our blind resistance to that fact just kills more people and drags out the issue.
*Those are not exaggerations for effect. I have personally seen mass demonstrations that killed multiple people over each of those issues. I'm sure there are more examples. I'm talking Tire fire barricades, burning of buildings, whole parts of cities shut down and running gun battles in the streets kind of "demonstrations".