Do I need to wait until there's no rain in the forecast before putting CGM on my lawn? Or is it ok if it rains shortly after it's applied?

It is okay to apply it before rain. In fact, it's great to apply it before it rains. If it is a downpour, you might have some of the CGM wash to lower areas... With organic fertilizers you are not limited with certain application rules as you are with the synthetic fertilizers.