Teeandcee, if it were me, I would wait until it's a little drier if your shrubs are in pots. They aren't going anywhere. I guess it depends on how crumbly your soil is, as well. Can you break up the wet soil you took out of the hole so that there will be no air pockets? I'd never plant in mud and when you water them in, it will be pretty wet.
JMO
Sunny

Thanks, Sunny. Yes, I can break up the soil. I'm just so eager!

I think you would only need to wait a day or so after it rains to plant shrubs unless it's a low spot and the soil is really goopy.
I don't wait very long, but then maybe I'm not very patient. lol I'm certainly not an expert. I was kind of curious what some other people would say about this. My yard is really rocky and it's easier to dig when the soil isn't dry.
Getting your shrubs in the ground early will help them adjust and get ready for summer which will undoubtedly be hot and dry.

We went ahead planted a pile of shrubs today. Some were in the shadier part of the garden so the soil was still pretty damp. I did a lot of crumbling. My forearms are sore.

The soil seemed perfect for planting in the sunnier sections....slightly damp but easily crumbled up.

I have to time this between rains and on hubby's days off (he's the official digger of holes), which is why I decided to go ahead and plant today and take my chances.

My yard is really rocky too, Christie.

I sometimes slip things in on a rainy day. When you have a forecast of a couple of days of dreary damp weather, you can stick small plants in here and there. The only clay I have here is top soil I bought. I wish you could buy good garden soil.