This isn't the cut-and-dried answer you'd probably like, but a) my Mazdas doesn't have any factory applied undercoating that a solvent would take off (but then they're not Miatas either), b) products like Simple Green usually don't remove such things if you don't let the Simple Green dwell very long and/or you don't scrub, c) it's sorta a catch-22 because if you don't really *degrease* the undercarriage if it needs it you won't really get it clean, but if you *do* degrease it you'll sorta run the risk of "degreasing the undercoating right off". Cleaning agents don't discriminate between good stuff (undercoating) and bad stuff (undercar grime). The only thing you can hope for is that the undercoating is more firmly adhered than the stuff you want to clean off.
I wouldn't worry much about it. If you *do* clean off something you want on there, I'd spray some wax-based undercoating back on the exposed places. I like the Wurth brand stuff. Just don't go spraying your Simple Green into inaccessible areas if you think there's anti-rust stuff in those places.