What can soak up moisture from a closed space
I'd be surprised that you'd have this much moisture from condensation, especially since condensation doesn't change the net moisture level, it's actually removing moisture from the air.  Double check for leaks, signs of corrosion on pipes, particularly at the joints, for caulk that is cracking in the showers, and the drain pipes.

Edit: One more thought, check where the bathroom vents are blowing.  It should be outside, but a lazy installer may have them venting into this space.

That said, without knowing more about the floor plan and what's above and below this space, it's hard to give a good suggestion, so I'll give several:


While you've got the opening in the wall, consider turning it into an access panel to more easily get to the plumbing in the future.  This can just be a few pieces of trim that are attached over the joint between the wall and cutout drywall.
If you want a vent in the wall, you can put in a simple hvac return grill.  That could also double as an access panel.
Insulate the pipes to prevent the air from interacting with the cold pipe and to reduce loss from the hot pipe.
If there's an exterior wall involved, check the insulation and make sure the vapor barrier (paper on fiberglass) is intact.
If you redo the entire wall, use moisture resistant wall board (green board may be more than enough, but they make stuff that's even more resistant).  You can also install an extra vapor barrier behind this.