Hmm, so far I haven't heard of anybody having issues with OBS + GTR2 of us streamers.
You are running Win 10?
With my limited knowledge the only reason I'd see GTR2 having an issue with OBS running is through shared memory access since there's no way GTR2 is accessing anything GTR2-related (unless you have it set up to save recordings or anything in the GTR2 folder)?
Anyway, a couple of things you could try is switching between Game, Window and Screen Capture as your source and see if it maybe works with a specific capturing method and again, always try multiple times since getting booted for suspected cheating can and will happen randomly from time to time.
If that doesn't work, maybe export your Profile and Scene Collection in OBS and reinstall it. Then check if it works before re-importing your old profile - if it does you can import your profile and scenes again and try again.

Sorry for not having a solution since I've never heard of this, but maybe the few suggestions there can help troubleshoot what the root cause is.