I'm repairing my bathtub/shower walls by removing the existing drywall and
tile to replace with new. After removing the existing drywall, I discovered
the thong and grove wall which is behind the drywall is damp. (I guess that
could have been predicated as there were cracks in the grout and drywall).
I'm not sure if I should let it dry completely before proceeding. My
worries would be problems with mold and mildew. The back side of the T&G
wall is covered with plywood and wallpaper. The process I was going
complete the tub walls is a sheet of polyethylene, cement board then tile.
Would I be trapping in the moisture if I cover it up now? If you say I
should let it dry, then for how long I should let it air out?
Thank you.

It sounds like the T&G is pretty well sealed on the back side.
Since you don't mention it, I assume there is no visible rot.
If it were mine, I'd give it plenty of time to dry out.
Perhaps you know someone with a moisture meter to test the moisture
within the boards.
I would consider sealing the wood and skip the poly layer.
TB