GTX 5w-20 seems to be the best warranty-safe option for the RX-8 in North America. It's all I run.
Oil temps, fuel dilution, and dirty combustion are all issues for rotary engines. That aspect screams synthetic. At the same time, the engine burns oil basically by design, so whatever oil you use has to burn cleanly. Some synthetic base stocks (certain PAOs IIRC) leave REALLY nasty residues when they burn, and there's no way to know which oils have those base stocks, so synthetics are out. You also shouldn't just throw in any old heavily additized oil, because those tend to have really ashy additive packs. You could theoretically go with an oil designed to be low-ash, but you might be sacrificing protection. So, you have a bunch of requirements that pull in completely opposite directions. And that's before you even get to the fact that these engines have a rep for spotty reliability in any case.
Given all of that, I'm not even slightly tempted to second-guess Mazda on oil for this app. Castrol GTX 5w-20 is what all the dealerships use, so it's what I use. Mazda does make a rotary-specific oil (a 0w-30 synthetic), but I don't think Mazda NA officially recognizes that oil for warranty purposes. So, GTX 5w-20 it is, at least for the next few years until the engine warranty runs out.
