There's two problems here. One is that the other player may not exactly like you taking their stuff without them having a say (like, they'd probably be fine if you convinced their dudes to follow you by a big speech, but would be less okay if you just took their dudes by an advancement option).
The other problem is that "co-ownership" of NPCs in AW is definitelly going to be weird. Some NPCs "belong" to you the same way something you can do by virtue of a more personal move, and yet they kind of don't, 'cause they're people. This interplay is all fine and good when there's only the MC and the player sharing control over the group... But I suspect as soon as there are multiple mechanical claims on a group, that'd you'd suddenly have to start caring very deeply about which player gets to roll first, which can get pretty frustrating.
Still, if you're interested in a story about shifting loyalties at all, I'm pretty sure AW can handle it, just not as well as straight-up ownership or moves.
I personally would like to see you play through it anyway, for science if not anything else. :)
So basically... Several ways you can handle this. Two obvious ones are just playing with the rules as they are and gritting your teeth through the hard parts, or just getting the gang from a non-troublesome source (fast-forward time if needed).
You can also repurpose a bunch of other AW rules to make dealing with this easier. If you go that route, more than one way to deal with it... I can think of two, either complimentary or independent:
1) Custom move with hold! Get hold either on a per-session basis (On session start, roll +x...), or a per action basis (When you sway your gang to your favour, roll +x). Then, during that session, you can cash in on that hold to do something that the other co-owner would disagree with.
2) Player-personalized front! The gang becomes a front that's about losing loyalty to the cult (or vice versa), and ticks down as usual unless action is taken, and becomes fully one player's or the other's once the front gets resolved.
And so on.