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Would it eat glue?
I use denture cleanser tablets for my boots. Put in one tablet each, fill with water, leave it overnight, rinse in the morning.
No more smelly boots.
Also used them in BC bladders, though I'm not exactly sure if they are really suitable for that purpose.
Listerine like most mouthwash is primarily alcohol, which is a pretty good general biocide, but something like rubbing alcohol or vodka would work similarly while avoiding the odorant and colorant stuff. Problem is it has to be used at fairly high concentration or exposure duration if you want good antimicrobial effect. That invites unfortunate chemical attack on susceptible components. There may not be any of those in your gear, but you might find out.
An interesting issue is the final fresh water rinse. Tap water is by no means sterile - so what have you now reintroduced? If you dry things promptly, it probably doesn't matter. If you can't dry something readily - like the bladder in your BC, maybe a final dilute alcohol rinse is a good compromise?...