Mud walls are far superior when compared to lightweight shower construction. An added bonus...with the reinforcing mesh wrapping the corners from wall to wall, there will be no dissimilar movement. So you can grout the corner joints instead of having them caulked. The only place where they can sort of get funky is the exposed edge of a mudded wall, where you can see the thickness of the mud wall. If your existing framed walls are out of plumb, then the mud man will float the new walls perfectly plumb. So on that exposed edge, your thickness of mud might vary, from 1" at the floor to 1-1/2" up high, for example. If your existing walls are out of plumb, it's an issue you can talk about with your man ahead of time.

I'm not certain of your exact situation, but if you're simply looking to hide the 1/8" difference between the drywall and the cement board... ...use joint compound to float the face of the drywall out 1/8" to meet the face of the cement board. Feather the 1/8" over the course of 12-18" or so and it'll be invisible. Prime and paint and no one will know. Mongo

I suppose you could Redguard it and tile away. Nothing ventured, nothing gained. Personally, I would rebuild it....but you say that's not an option. We really don't know if there is a vinyl/rubber liner under the mudbed...nor do you, apparently....and a redguard membrane, if that is the case, is superfluous. At this point, just paint the stuff on and tile away. It may last awhile...it may last forever. You pays your money and you takes your chances....

@zealart - You are correct. As President Reagan said, trust but verify. I just finished a remodel including gutted bathrooms with new showers installed. I spent a lot of time on the Board reading about shower construction and horror stories. I followed links posted regarding shower construction. Much of it went over my head but I retained enough information so that I was able to ask reasonably questions regarding the materials used and how my shower was being constructed. I also checked out work done (including showers) by my designer and GC. All efforts put into researching and learning as much as possible will get you the best possible end product. And not just in terms of actual construction - but taking the time to read copiously enabled me to learn about how I wanted my space to function and what products or design elements could get me the results I wanted in both design and functionality. I did have a great designer but it really is more of a partnership as I needed to tell her how I wanted my space to work - and sometimes there was stuff I read about on this forum that I was able to tell her about :-) - like my toe kick step drawers. I also live in an area in which stuff is RIGOROUSLY inspected at every step by the City. My shower pan had to pass a 24 hour flood test for starters. I took pictures of my showers at various stages of construction which show the waterproofing and materials used. I do know that my shower is sloped - I can even see where it slopes even more markedly by the drain. There is no puddle or even small remnant of water left when I finish. And I doubt any slime or mold is growing anywhere either since my automatic fan runs until it registers a low humidity in the bathroom. FWIW, my curbs appear to be some kind of concrete and the curb is solid surface - constructed from a remnant of my counter and my bench is constructed of the same material. From everything I have read, solid surface for curbs and horizontal surfaces is recommended over tiles.