There are two classes of CBU out there, those that are all inert (mostly cement and aggregate), and what is referred to as fiber-cement boards (HardieBacker is one of those - it contains up to 15% cellulose).
There are two sheet membrane manufacturers that have had their membrane installation certified for use over plain drywall: Schluter's Kerdi (been around for about 25-years), and Laticrete's Hydroban sheet (not their liquid - sheet first available mid-2014). So, the one with the longest history by far is Kerdi.
While some places do not require a liner on a recessed pan on a cement slab, I think that it's a major mistake. Be aware that while a liquid applied waterproofing can work, it is, IMHO, a lot harder to do it right than some other methods. It's just too easy to end up with a pinhole or thick and thin layers that ultimately, don't work quite as designed. If you choose to go that route, make sure that you pick up an (inexpensive) wet film thickness gauge, and ensure two things: you know how to use it correctly (you'd be surprised how many people don't), and that you get your wet layers (they all require at least two) applied within the min/max wet thickness. Give two people the same roller or brush, and you'll get significantly different coverage rates. The liquid stuff needs the minimum at least, and exceeding the maximum can lead to failures, too. Watch the required timing on application and the wait before flood testing or you'll ruin things right off the bat.