humidity should not affect the leather, I would say quite the oposite... maybe the hardware parts on some strops could be affected in a very humid environment, but most strops have hardware that resist humid environments with no issues.
havig said that, my strops hang in my Office... just no way my wife let me keep that many strops in the bathroom... plus, my razors are also in my office (toddler's safety), so.. the stropping always takes place in the office.