While watching a pride of lions, it started to rain. Hard. The lions were clearly not thrilled getting wet, but they tolerated the rain and stuck around.
The only time we saw rain of any significance was in Masai Mara, and both days around the same time and intensity. It reminded me of summers in Colorado. Wildlife and humans alike, we all patiently waited for the weather to clear. Our guides said lions would play after the rain, and they were not wrong.
When it rains, the safari is paused and everyone patiently waits for it to stop, wildlife and humans alike.