First off, I've never seen a difference between shooting in the rain, and shooting on dry days. The biggest issues I've had, are long shots during the middle of summer. The "heat waves" causing refraction can play hell with seeing your target.
Rain makes up 0.2% of air volume during a 2-inches-of-rain-per-hour storm. (With 0.016 gallons of water falling through a cubic foot {7.5 gallons} of air per second.) It makes up far less than that during normal rain storms.
You have a 1:500 chance of hitting water in a one cubic foot air space (2"/hour) during a 1 second time interval.
Remember - The human brain makes us see things that are not necessarily real. It may look like a wall of water, but it's a bunch of individual rain drops. The streaking is a processing effect, done by our brains, so we have time to "see" the rain - rather than the brain only acknowledging it subconsciously.
To look at the odds of hitting water, let's look at only the bullet's path.
Imagine the bullet will travel through a "cylinder" of air.
With a .308" bullet, we need to find out how long this cylinder will be, to have a volume of one cubic foot.
1 Cubic Foot = 1,728 Cubic Inches
The volume of a cylinder is calculated as:
Pi*radius^2 (of circle)*length (of cylinder)
The radius of a .308" bullet is .154".
Pi(3.141)*.154^2 = 0.234 square inches.
1,728 cubic inches / 0.234 sq in = 7,382.5 inches
So, a .308" diameter cylinder needs to be 7,382.5 inches long to contain one cubic foot of volume. (7,382.5 inches / 12 inches per foot = 615.2 feet)
Which means.... your .308" bullet can travel 615 feet or 205 yards with a 1:500 chance of hitting water. Move closer to the target, at 100 yards; and you have a 1:1025 (0.0975%) chance of hitting water.
If it's only raining 1"/hour ... those odds go to 1:2050 (0.0488%) at 100 yards.
And that's not even figuring the adjustment for bullet flight time. Most bullets won't take a full second to reach the target. Therefore, they won't have a full second's worth of exposure, and the odds of hitting water are decreased even further.
For example (simple calculation with constant velocity):
A 2,100 fps bullet will reach a 100 yard target in 1/7 of a second (2,100 feet per second/300 feet = 1/7 second).
That means the odds of hitting water drop to a 1:7175 (0.0139%) chance of hitting water.
The odds are in your favor.
*Some of these numbers were rounded to certain decimal places.