No. At least not any more loosely than any game (D&D) that I play at the table compared to that which is published by WotC. Heck, simple name changes have gotten around WotC IP for years. I know I have purchased more than a few "serpent people" in my time. I don't think that has affected compatibility one bit.
Then "compatibility" means something a hell of a lot stronger when I use it than when you do. "Compatibility", to me, means that you need do nothing, or very nearly nothing, and the work in question can freely use any parts from the official rules that it likes as starting points for its own content.
What you're talking about, to my eyes, sounds like (for example) what Drop Dead Studios has done with its Spheres of Power and Spheres of Might rules. They start from the most basal fundamental rules...as in, what "attack rolls" are and such...and then build an entirely different system on top that may or may not have any proper compatibility. The GM running said content has to figure out for themselves whether any given piece plays nicely with any other piece, and has to do a lot of translating, comparing, and (occasionally) retooling/reworking to ensure that the alternate system and baseline system actually work together.
It would be like saying that USB-C is compatible with USB-A, you just need an adapter for it. At least as far as I was aware, most people who say two plugs are "compatible" mean you can...y'know, actually
plug in a connector of one type into a socket of the other type. The need for an adapter is, itself, what makes it not "compatible" in that sense, but rather, well, "adaptable."
So if you mean that these things can be
adapted to be used with actual 4e, I mean sure I guess? But anything can be
adapted. It's just a matter of how hard you have to work. A "mostly already adapted" thing is still a pretty long ways away from being actually plug-and-play.