Hi Paul, welcome to the forum.
Drywall is the manufacturer's recommended substrate. Plain drywall, not greenboard. Greenboard is regular drywall with a water resistant coating applied to it. You might think that it would be slightly better than plain drywall. But the water resistant coating is extremely minimal. And the fact that the coating is something of a "bond breaker" that diminishes the bond to it, it's not worth using. I'd only use greenboard if the code in your municipality demands it.
Some folks really, really want to use cement board. If you feel compelled, go ahead. But the membrane is indeed waterproof and you should feel comfortable using the manufacturer's recommendations when they are the folks issuing a very solid warranty.