I wouldn't worry about it either. I've been running synth gear oil in every car I buy regardless of manufacturer's specs.
I just finished switching the 318i to full synthetic, I'm trying Valvoline 75w90 gear oil in tranny & diff, Quaker State 5w30 in the engine. I'm not holding my breath for more power, but I am hoping to get a bit more economy. Next up is pulling the p/s and a/c. Then maybe a new electric fan?
I've never tried the Royal Purple or Red Line. Had a little sticker shock at Advance looking for the Purple. Any difference between them besides price?