I guess it depends on how you approach things, but there could be ways to prevent ill effects if no airflow is a worry. I've also seen many stocks ruined by oil seeping back into the wood from rifles stored recoilpad down. Of course they were over oiled...
I can recommend Bore Stores for storing in humid climates and for safes that are very full to prevent dings from other rifles.
A friend of mine stored the rifles muzzle down with each muzzle in a little pill bottle of oil.
By the way, I run a dehumidifier in the more humid months and switch it on from time to time in the dry months too.
A soft pad under a recoil pad goes a long way towards preventing damage too and I would certainly recommend at least that.