Originally Posted by twinkie
Cedar woods contain oil but not acid. ... There is a chemical in the wood but it is not acid. Acid is in cardboard, paper and tissue paper and comes from the paper making process.
With all due respect to your DH, acids and oils are present in all wood and wood products, cedar included. Acid may be increased by the paper making process, I don't know, but it's definitely present within the tree itself before any processing. It's one reason why tree mulches, even cedar mulch, increase the acidity of your soil.
To the OP, some here have had good experiences storing in cedar or other wooden chests, some have not. Even unsealed wooden shelves and corrugated cardboard boxes can discolor and deteriorate the fibers of textiles. Examples have been given on several other threads over the years, some are truly heartbreaking. Only you can decided what your risk tolerance is.