Heres my experience with rain water. When i add my nutes to rain water, i always have to bring the pH up because it goes too low for my soil plants. When i add my nutes to tap water, my pH goes to 6.4 almost everytime and thats where i leave it.
I find filtered rain water works great in my hydro experiments. After i add my nutes the pH is basically right where it needs to be for hydro. I find the pH doesn't fluctuate much either when i use the rain water.