"What specific groups are we discussing here?"

Every group that has an "AQ" added as a prefix is made up on nationalist insurgents that have bought into the AQ message and franchise. These groups in turn have roots that reach into the perceptions of poor governance and western manipulation within the respective populaces they emerge from. Help those populaces address their reasonable concerns, target and manage those perceptions, and one begins to disempower the AQ agents conducting UW, and also the more radical members of the nationalist groups who are more committed to their personal goals than the overall good to the populace.

"True enough, but how is this related to AQ? AQ certainly isn't fighting for liberty, nor are they broadly perceived to be fighting for liberty."

By whose perception? AQ has a regional agenda, which is why they are a non-state UW headquarters rather than an insurgent organization. Sure, they specifically want to depose the Saudi family and specifically want to humble the US, but all of that also contributes to a larger goal of leading and leveraging the distinct quests for liberty among a wide range of oppressed Muslim populaces across the Arab world. Now, if AQ ends up in some sort of leadership role over all of these liberated states in a union that somehow does conform to traditional "Caliphates" of eras past, then no, I do not think there will be much "liberty" in that for the affected populaces. But if that is the case, then AQ loses their non-state sanctuary, they become the counterinsurgent rather than the UW instigator, and become very vulnerable to both outside state action as well as internal insurgent action. But I do believe that a regional liberty from western influence and western supported oppression is very much a part of their platform.

"I've seen no credible evidence"

For years Saudi-based charities, who draw contributions from across the populace base, have supported this movement. Every liberty-seeking movement is typically such, where the vast majority of the base of support is largely passive and beneath the surface. One can only assess the size of that base by other indicators.

The current rash of popular uprising in the face of certain consequence is such an indicator.