With regard to rainwater:
I am a huge fan of it. I have collection barrels at my downspouts. Of course it does wash off the dust and dirt from the roof, along with any loose asphalt prills which are on the shingles, but I still think rain water is unsurpassed with any tap or filtered water. My rain water registers at about 6.0, which is about right. The only time rain water absolutely needs to be processed through filtration is for potability. If you had a huge cistern and wanted to live off the grid, you can collect 20,000 gallons and pump it through a filtration system. If you only use this water to flush toilets or water plants, it is totally safe.
There is a product I tried out last season to see if I could cut down on the sludge at the bottom of the rain barrels. It comes from Garden's Alive (look it up) and it is a biological tablet I put into the barrels and both our ponds to keep the bottom sludge manageable. It actually worked and I believe added beneficial organisms to water which otherwise could have easily become anaerobic.
I'm making it more complex than it need to be. No, for plants you do not have to filter rain water. Actually, when a thunder storm waves through, and if a lot of lightening is involved the rain water can capture the nitrogen which has been fixed in the atmosphere via the ionic exchange of an electrical charge from the lightening. Did you ever notice your home garden and trees looking magnificently green and turgid after a thunder and lightening storm? It's the fixed nitrogen from the air! Amazing how nature does this.