Well, firstly, the burden of proof would be on the person asserting that two styles are so utterly incompatible that they cannot both be supported meaningfully.
Second, many people make a great deal of the idea that D&D does in fact try to be many things to many people--perhaps not all things to all people, but a pretty sizable chunk on both axes. I mean, 5e was literally billed to us, in part, as the "big tent" edition that was supposed to offer stuff for effectively everyone. I am of course rather convinced that it failed miserably at that task, and that that is why they quietly stopped talking about it about 2/3 of the way through the D&D Next playtest, but that doesn't mean the goal couldn't be achieved, just that they failed to do so.
Frankly, a lot of the things people claim are totally incompatible aren't. Supporting them doesn't even require the level of "modularity" that playtest-5e originally was claimed to (potentially) offer. E.g. you're gonna have your work cut out for you to explain how purely opt-in "zero level" rules would be incompatible with other styles of play.