I have had 3 RX7's. In street driven applications, regular dino low-ash 5w-20 or 5w-30 should be fine. You can even use the hydrocracked Motorcraft stuff if you'd like if you have the absolute need to use a synthetic. Otherwise, for racing applications and sustained high-rpm, you can use synthetic low-ash oils.
Some feel that the 5w-20 was too thin for the RX-8 and had side seal and housing failures; using thick oils does not have any negative effects in a rotary, the "crankshaft" portion is partially gear-driven and does not like thin stuff, and you also won't see any horsepower/mileage losses in going to thicker stuff in a rotary, in general.
In my street rotaries, I used a low-ash HDEO 15w-40 diesel oil. In the racecars, same stuff or Valvoline VR1 20w-50.