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So, I’ve noticed that a couple of my rear mechs have quite a bit of lateral movement.
One is XT the other Sram NX. I can’t see anywhere obvious that I can tighten. On the XT one do I need to delve into the clutch mechanism?
Presumably you've checked the main single bolt that bolts it to the hanger?

I found a some play on my slx 12sp mech when I was servicing it. Turns out that if you back off the lower limit screw too far there is a dead zone where the spring becomes loose and you end up with play. That confused me for a bit so worth checking it's not that.
But as above, first suspect would be the hanger bolt.
On SRAM this is a 'feature' and nothing to do with them exploding at random.
all of mine have a tiny bit of wiggle play... i thought/assume it's just normal
All of my SRAM (GX, NX and XX1) have had some lateral play from new. If it's not impacting performance, then don't worry about it.
Thanks all. Def not at the hanger. Feels like it’s around the clutch mech. I have one on another bike that doesn’t wobble…
If the mech hanger screw is tight then it’s almost certainly the pivots on the parallelogram of the mech its self… for which you can do absolutely nowt about as they’re pressed in.
My xt has a bit of play, it’s not great but it still works
It’s worth having the mech off and service if the clutch system. I didn’t realise you could (easily) do this and it’s saved two mechs. From a mechanism that won’t take up the chain tension to almost feeling brand new in about 10 minutes!
It was a gmbn vid on YouTube with Doddy that showed me how to.
Edit
I had a lot of play in my rear mech , eventually traced it to wear in the hanger allowing the mech to pivot instead of being square on. New hanger fixed it.