Each to their own, I suppose, Ed. I use RO water because it's what I have, and I wouldn't drink our city supply, so wouldn't use it in making cheese, however small the amount used.
Jbrewton, a majority of sources, you'll likely find, recommend distilled water. Most important is to use dechlorinated water, however you get this, as chlorine really does wreak havoc. My use of RO water is really just a preference - but then I'm a fairly rigorous purist (i.e., a PITA to many cooks who've worked in my kitchens).
And many do feel the water temp affects the renneting, so prefer to use cool water. I don't consider it "overthinking" or "WAY" over the top, but again, each to their own. Good luck.