How often is this going yo get used as a shower ?

If everyday, INSIST on the aqua defense or another liquid waterproofer.

And, be sure it is applied to the proper thickness. They don't work when applied too thin , and don't like being applied too thick. You'll need a wet film gauge. Paint stores have them.

I can give you the "technical" answer.

Aquadefense can go over gypsum board, but only in "approved areas".

Building code (IRC, etc) prohibits using paper-faced gypsum board products as tile backer boards in showers and tub surrounds, even if the paper facing and the gypsum core of the wallboard are moisture resistant.

So technically? No, Mapei does not recommend, authorize, or warrant Aquadefense over gypsum board in wet areas.
People have brought up that Kerdi can go over gypsum board in a wet area, so why not other topical membranes? Above being just a waterproofing membrane, Kerdi is also a vapor barrier, whereas Aquadefense is not. Aquadefense is just a waterproofing membrane. Plus, and more importantly, Schluter (the manufacturer of Kerdi) has paid for testing to have Kerdi certified for going over gypsum board in wet areas. I used to have to present that certificate to building inspectors when using it in that application.

If you want a code-compliant shower and you want to use AD, then have them remove the gypsum board and install 1/2" cement board (or any other code-compliant backer board that is compatible with AD) in its place.

Or you can leave the gypsum board and have them install Kerdi over it as your membrane, that'll be compliant as well. But if your building inspector is unfamiliar with Kerdi/drywall, you may need to present the certificate, it's vailable from Schluter. Although something tells me that if this guy is installing paper-faced gypsum board in a shower, either he's clueless, or the building department is, or that this work will not be inspected. But that's beyond this post.

So the short story that is code compliant? Either use Kerdi over the existing gypsum board or use Aquadefense over cement board. Your safest bet is AD over cement board.

Personally? I'd not want to "force" someone into using a product like Kerdi for the first time. It's easy to install, but it does require attention to detail. On top of that there are certain thinset that Schluter allows and disallows with Kerdi. Meaning that when you use Kerdi, you have to follow the rules. Your installer doesn't seem to like rules.

So I'd recommend they pull the drywall, install 1/2" cement board, then use Aquadefense over that. It's within the realm of your installer's ability and they are materials that he is familiar with.