Yes it's very safe to jump start a car or other vehicle while it's raining out.
A car puts out 12 Volts which is not enough voltage to do any or much harm to you should you get shocked by it.
That's way less voltage than what goes through your houses wiring system so it's completely safe to jump start the car in the rain.
You might get a tingle feeling if you do happen to get shocked but it will be harmless to your body.
If you don't feel safe jump starting the car in the rain then someone else may do it for you.
Towing companies and other people jump start cars and other vehicles in the rain without a problem.