I've got my babies outside, temps are fine now. I've been careful about over watering. What about the rain? I have no way to protect them all or bring them inside when it rains. How do I prevent root rot? I use 4x4x9" pots w large drain holes in the bottom. I use 50/50 promixHP and pine bark mulch. Am I worrying for nothing?

A lot depends on temperature. Cold and raining is a lot worse that warm and raining. in warmer weather they will dry out faster, obviously. 1" of rain is probably somewhat equivalent to you watering them. 3-4-5-6" of rain is too much.

How about a tarp type lean-to over them? I would find someway to minimize the impact if it is going to be an issue. Maybe picnic benches, strips of wood and a tarp. Time to get creative and think outside of the box.

Here is something to try....taka a piece of tin foil large enought to drap around the top of the pot and gently crinkle around the cutting.  This will enable the top to enjoy the rain but will keep the soil in the pot from gaining too much water.

if your soil drains well, rain water will drain out in a day or less. minimum impact. but if it rains while your figs are swelling... that can be a problem. last yr while figs were ripening, we had none stop rain for days. totally destroyed my main crop.

I have cuttings (aka figlets) in 1 gallon nursery pots with 60/40 perlite/potting soil.  The only time I baby them is when night temps are predicted to get below 40F (like last night).  They have been out in 2-3 days of rain with little ill effect.  One of two plants don't look happy (especially Hardy Chicago) but a few days later they are fine.  I'm sure the figlets don't mind the extended days of rain since I am still using a fairly good draining soil mix.  When I move up to a 3 gallon nursery pot and decrease the perlite percentage, well that may be a different story.