Almost every firearm that comes through our lab gets processed for prints prior to firearms analysis, they use dye stains, and we have never once had any issues.
I double checked with them this morning, and they use both methanol based and water based dye stains. As a general rule, they will use water based on any firearms that have wood on them (rifles/ shotguns with wood stocks and forends, and pistols/revolvers with wood grips) and the methanol based on everything else.
There have probably been thousands of guns processed this way and I've never thought there was an issue. Not to say that we haven't had guns with rust, but it's never been rust that I thought might be attributed to any chemicals LP uses. And depending on the agency and the year the firearm was submitted, they may be packaged in plastic bags or cardboard boxes. With that said, they are dried before they are returned to evidence intake.
So if anyone is seeing rust they think might be because of a water based dye stain, it might likely be because it's not being dried all the way. And while I've never done latents--so this statement is purely an observation--I'm thinking that "gunk" build-up might be because they are going overboard with the dye stain. It's a rare occassion when I can even tell it's been used (i.e. end of sawed-off stocks where there is exposed, untreated wood or occasionally in a crevice).