Yes, there is shared plumbing between the engine groups. While all oxygen feeds are independent*, all of the methane feeds have to be sourced from the methane downcomer; the methane tank is on top of the oxygen tank, and it has a long tube in the center to feed the methane downwards.
If a lot of engines are shut down at the same time, there might be a water hammer effect in the downcomer, which could damage the downcomer and the distribution manifold — or at the very least it would require extra reinforcement that could be avoided with a staggered shutdown.
Schematic overview showing the methane downcomer (green) in the center of the oxygen tank (blue).
The manifold. This is for an older version with 28 engines, but the current version is similar.
Here's a view of the plumbing (again for 28 engines). The blue pipes are open and just suck in oxygen from the pool at the bottom of the tank. The green pipes connect to the manifold (not pictured).
Additionally, as Russell mentions, there might also be a jolt from shutting down too many engines at once. More important than the payload shocks is that this could cause problems with the ullage. SuperHeavy needs consistent positive G-forces during hotstaging to make sure the engines don't suck in air bubbles, so the shutdown probably needs to be gradual enough that there's no excessive splashing inside the tanks.
As Russell mentions the turbopumps are independent, but it's possible for SpaceX to shut down or throttle down an opposing engine to maintain thrust balance. It's unclear if this happened in flight 4, there was an opposing engine that seemed to be downthrottled but it wasn't exactly opposite.
Still from flight 4 showing a throttled engine in the top left. Source from SpaceX via landru. Note how the throttled engine is not exactly opposite the one that was shut down.
* The current 33 engine version of SuperHeavy has the inner 13 engines connected to the oxygen header tank. It's unclear if it's being fed from there at all times or not. There might be some risk of water hammer in that too, but it should be less severe than the methane downcomer.
Current 33 engine SuperHeavy plumbing.