Replay mod version: replaymod-1.16-2.3.1-7-gdc9fcb1
Carpet mod, fabric, and fabric-api are all on current versions. Crash log in provided txt. I don't know enough if this is a problem with replay mod or carpet mod.

Carpet Mod: https://github.com/gnembon/fabric-carpet/releases

repalymod-crashes-with-carpet-mod.txt

I had a long look at this and I'm really not sure who's in the wrong here.
The easiest solution is a specific change in carpet, so I've opened an issue for it over there: gnembon/fabric-carpet#341

Should be fixed as of Carpet 1.3.33

Confirmed working with Carpet 1.3.33. Thank you for looking into this.