I've taped my blued 870 for 30 years...........
if you count this upcoming spring season. I hunt hard, say 30 hunts out of a 45 day season on a good year. Taping was about the only option short of paint before camo guns.
I've used both the HS type tape and the cloth tape as well. My drill is to spray the shotgun down w/ WD-40, and wipe it off, allow the gun to dry for a bit, and then tape.
If the gun gets moderately wet, as in dew or hunting after a rain, I hose the whole gun down with WD again, very liberally. If the gun gets really wet, as in hunting in a rain, I strip the gun of tape, re spray, and re tape.
I do not allow the gun to remain in a case between hunts, wet or not.
I have had only a few instances of rust under the tape in all those years.
I always remove the tape at the end of the season.
Taping is sort of a pain, but I've carried that 870 so long and so far, its just part of my spring season. I can get a couple of seasons out of a roll, as remove the glossy wood stock and fore grip, and add painted synthetic same, thus do not have to tape wood.
If I were to buy a new, dedicated turkey gun, it would have a camo or matte finish, to avoid all the above.