I would say it's not good because algae lives on unclaimed nutrients and there really shouldn't be any nutrients for it to subsist off of if you're growing CPs. Algae growing over your moss will also block the light getting to your moss.
As far as the aquarium goes, good luck, once the water goes green it's pretty hard to get it back to clear.
If you don't have any live aquatic plants you can try keeping the lights off for a week or two (the fish won't care) and do several big water changes during that time. The absence of light and reduction in nutrients
should clear it, but green water is very pernicious. There's nothing like seeing the aquarium lights pop on in the morning and being greeted by a big green cube of lime jello with fish swimming in it.
If you have live plants do you have roughly 3 watts of light per gallon? You must use bright lighting for aquatic plants to trigger their water scrubbing capabilities. But first the green has to go so if you have live plants you'll just have to do water changes over and over until the nutrient levels drop down and the plant's can receive light again, and make sure they're getting bright enough light and they should be able to help clear the last of it for you.
If you have a filter which allows you to use charcoal or other bagged media get some Phosphorous removing media (looks like white aquarium charcoal), this will help while you do the water changes.
I would run some tests on your rainwater before using it anymore, doing water changes using more of this same source water will probably not help. Fish stores will usually test your water for free. There must be some source of pollution which is causing high nutrient levels in the rainwater you're using. Particularly test for Phosphorus.