Like several others, I use the same tape on rainy days that I use on snowy days, sunny days, dusty days, etc. I thought your question was going to be how to get tape to stick when the barrel is wet.
My current muzzle tape is Scotch 88 (or 808 ?) and it is an extra sticky black electrical tape. My progressiveness has not yet attained blue tape. I did a banana peel slip into muddy water over my head while stalking a moose a couple of years ago, and though it was not raining the tape on the muzzle paid for itself that day.
One other personal preference: I use minimal tape to minimize any influence it might have, though I have never detected any influence on bullet flight. An old wolfer first got me to using tape 25 years ago. He cut round spots of tape exactly to fit the crown of his rifle and stuck a half dozen or more on his butt pad or stock. My current ones are a spot with a small tail of tape on each side.
