I only needed to participate in ONE lost blood trail in the rain to make it a "no-no" for me...
...however, there are exceptions.
I tend to think of early season, b'cause it's NOW early season...so much underbrush...hard to find where they travel w/out blood trail... If it's raining hard enough to wash off the trail, I hang up the bow. If it's early, the temps mean I need to find that downed deer shortly to avoid meat spoilage. I love my deer meat...
Time of day is another variable. Early day shot means more time to find it... cool temps, vs. warm temps...etc.
now if it's later season, frost has killed brush and leaves are down... it's cooler and I can see a lot better, trail through leaf disturbance... etc, I might take the shot if the country was more open.
Seems there are a lot of "variables" to consider
Generally speaking, I won't "SHOOT" in a steady rain...but often will be out there when it's intermittent.