I will hunt, and have hunted, in a light rain with my flintlocks. The guns have never failed to fire; and one one of those drizzly days I did take a deer. I use a greased lock cover, and carry the arm with the covered lock under my armpit, under my capot, with the barrel always sloping down. I also change the priming at least every hour. And I often seek the cover of a nice big tree.
When it's raining more steadily, I do what I imagine my ancestors would have done. Stay in, stay dry, and don't risk illness.
I wouldn't participate in a shoot in the rain. The more you expose your gun to it, the more chance you have of problems. And just standing around in the rain has never appealed to me... no matter what I'm doing.