Ok I just read their installation manual. They mention that every penetration must be sealed and do not provide any advice on how to do deal with mounting screws. . They do however come off as a company who would be happy to tell you why their product is best for everything and how to use it.
I've also read the installation manual for the shower wall and door. The wall and base are intended to be installed with 5/16 inserts which are provided. This type of fastener implies to me that even if the Kerdi stuff isn't as strong as lumber, once it has tile on it for the rigid wall of the shower you should be fine, just use silicone to seal when you put the clip down and possibly a touch under the screw head before you finish driving it. The inserts work by expanding when the screw is driven through them, so to pull out, either they have to break or they have to pull out a section of drywall and tile significantly larger than the screw. If the Kerdi wallboard is rigid like and as strong as drywall, the inserts should be fine, but from a video of the Kerdi curb, it appears to be foam, and if it's not adequately rigid, you'd be relying on the pullout strength of just the tile so you should add wood backing, forego the inserts, and use longer screws if necessary. At the bottom you don't need much pullout strength, mostly shear strength, but if you can't trust the full strength of the insert, you need a better fastener, so you should inset wood into the KerdiKerb as suggested by Quoc Vu or build the curb the traditional way to make it more solid. Also as suggested by Quoc Vu, you can test the pullout strength of one of the inserts with a cutoff piece of the curb. Drill a 5/16 hole and pound in an insert, drive the screw in and pry it out with a prybar to see what breaks. It should still be much harder to pull out the insert than to pull out just a screw. If the insert and screw come out, it means the insert couldn't expand. If it does damage and widens the hole, it expanded but the material isn't strong enough. If it tears out a huge chunk it's probably adequate. If it is hard to pull out it might be fine. You can pull one out of ordinary drywall and out of wood to compare. Wood doesn't allow the insert to properly expand. If you are screwing into wood, don't use the provided inserts and if you use the Kerdi curb, get your own longer screws as the foam is quite thick. If you don't mind installing wood backing, it is significantly stronger than using inserts, but the people who designed your shower door designed it for inserts, which shows a lower expectation. They probably designed it to work with inserts because they wanted the option of installation in concrete. The inserts provided in your product look like this:
They look something like this in real life:
This is a type best for thin or semisoft materials like drywall. The split allows the sides to spread out and spread force well. If you do a pull out test and you find that the material was hard enough to prevent the insert expanding, you can use an insert specifically for hard materials like this:
For the shower door it's a bit more complicated. They specifically state twice in the manual that the shower door is heavy and must be screwed into stud or a 2x6" board mounted behind the wallboard for the purpose. They then go on to describe drilling holes and mounting the same inserts used for the rigid wall and screwing in to them, completely disregarding the stud requirement. Sounds like an extra requirement from a smart proactive person, and then a procedure slapped together by someone less diligent. I would suggest you trust the guy who wrote the extra requirement and acquire screws with the same head that are long enough to drive into the stud. There is a chance they actually decided the inserts would be OK and used them intentionally, and you could call them to find out, but it may be easier to just go with the stronger requirement.
Edit: Made some edits after Quoc Vu caused me to reconsider and further investigate. The advertising materials call the Kerdi curb load bearing, but it's foam so I'm concerned it could have too much give even with wood backing. If the bottom mounting brackets concentrate enough force to bend or compress the Kerdi curb, the tile or grout will crack and you would have been better off with wood framing and only 1/2" of more vulnerable material in the form of drywall.