I downloaded your existing apps and all of the XSLT files are 1.0. Can you confirm that you are re-implementing the XSLT operations as 2.0? And can you confirm that you absolutely, desperately need XSLT 2.0 support and no other solution will suffice? XSLT 2.0 is usually only used via Java, in a server context, and only in a handful of very specific, XML-friendly industry domains.
This is the best reference that I've seen for XSLT version support: (https://stackoverflow.com/tags/xslt/info/)
I don't know what you mean about that external C library that is no longer acceptable in the App Store. The only reason I could think of would be a GPL-licensed project. If that's the case, then the App Store isn't the problem, it's the license. The GPL license is designed to prevent you from using the code with Apple platforms. Releasing such code in the App Store would be a violation of the license. That makes the app illegal and Apple doesn't allow illegal apps in the App Store.
From my casual inspection of your app bundles, it seems that XSLT may only be a tiny part of your apps. It doesn't sound like trying to support XSTL 2.0 is worth the effort. If there was something specific you need that XSLT 1.0 doesn't provide, maybe you could implement your own EXSLT function.
Anything that Apple provides is going to be XSLT 1.0. There really isn't any WebKit interface per se. I think that just refers to the standard XSLT HTML stylesheets that I think all web browsers support. There's no point in trying to do XSL via Javascript in WebKit. That's just a Rube Goldberg architecture.
My software makes very heavy use of XSLT and all of it is XSLT 1.0. You can do pretty much anything in XSLT 1.0. Certain things may be easier to do in XSLT 2.0, but the effort required to support that far exceeds the gain in convenience. And if you are willing to write some EXSLT, then there's virtually nothing that you can't do in XSLT 1.0.
Apple has some native XML and XSLT APIs available: (https://developer.apple.com/documentation/foundation/archives_and_serialization/xml_processing_and_modeling/)
Personally, I don't use Apple's APIs. The DOM processing APIs, which include the XSLT logic, are macOS-only. It was quite easy to implement my own, more powerful, wrappers around the lower-level APIs provided by libxml2 and libxslt for parsing XML and transforming XSLT. I do all of the XML generation logic on my own. I've only written EXSLT functions in Perl, where they are very easy. They are probably much more difficult to implement in C.
I certainly wouldn't consider Apple's Objective-C API, or the lower-level C APIs, to be "unsafe". They are C-based, so you have to be careful. You may get some minor memory leakage in instruments, but not enough to worry about. The biggest problem is that they are Mac-only and essentially forgotten. Apple doesn't pay much attention to them and neither do most app developers. Using the lower-level C APIs provides some insulation against potential deprecation and removal of the Apple wrapper APIs.
I'm not sure what you mean about a "clear statement in the reference documentation". XML, and by extension XSL, are not "popular" technologies, in the social sense. While they are widely used in many industries, you won't find much about them on the internet except as fodder for mocking older developers. There is very little overlap between XML and the practice of most app developers for Apple platforms. It is safe to assume that everything is XSLT 1.0 and will always remain so.