For us, it depends on what type of rain and the temps. If you're talking a tropical storm bringing inches of rain, we'd change plans. If it's raining and temps in the 40s/50s, we change plans. If it's off and on rain with temps in the 60s or 70s, we're good. In fact, we've found that on days like that, the crowds are lower and we do/see more! Rain jacket, poncho, umbrella - work fine for a day.
As for predicting what you might get through an extended forecast? Good luck.