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?

Since I can't count on the amount of rain I get, I would apply without rain and then water it down. I would not drench the soil, but only a surface watering to keep the dust down.

There is some so-called research floating around about the efficacy of CGM that is negative about the product. In these trials there was no watering done at all. It's my experience that the best results come from watering the CGM in well and then allowing a dry period. I'll do a report on the "research." It looked at first glance like a typical "lets prove this stuff doesn't work" project. More later.
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I am waiting for the right time also. Living on the coast it is constantly having spells of dry and wet, usually one or the other every 4 days or so.

My question would be....if I put CGM down and water it in as Howard suggests, what will happen if it rains 2 days later and it washes it in even more? Will it wash away or will it have done its effect within a few days?

Just wondering.

I did put mine down and it rained a few days later but not much. I watered again about 4 days after it rained since we're not forecasted for rain again for another week.

I think you'll be ok unless your yard is not draining well and you have a lot of run off.

I applied CGM last week. I watered it in well, then about 5 hours later it rained about 4-5 inches and I was concerned that it all washed away. Do I need to reapply?

That's not true. Unless the rain washed off an inch of soil, the fertilizing you have done will still be effective. That's one of the great advantages of the organic program. If you want to add a light application as a supplement, that's fine but another full application would be a waste of money. In addition, too much organic fertilizer, espescially a powerful one like CGM can cause some of the same problems that the synthetic stuff causes.