Surely there's a sense in which the
precise meaning of "greedy Frenchmen" still exists? It's obviously a bit difficult to discuss without context, but entirely discarding the
accurate meaning based on there being "questions about the motive of the speaker" seems, I dunno, hasty? "I helped my uncle jack off a horse" still has two meanings, even though only one of them is the punchline.
My point, linguistically, is just that "<adjective> <group>" paradoxically both qualifies "<group>" and also links "<adjective>" and "<group>". I think that is just how language works, (I'm admittedly not a proper linguist and kind of freestyling). I think that's true of "greedy Frenchmen", "fundamentalist Christians", "fundamentalist Muslims", "toxic masculinity", "gold-digging women", and, well, just in general.
Whether it matters, whether you care, and what you want to do about it, are separate questions. But I think it's useful to understand that language functions that way, whether you like it or not. I don't think these phrases should be verboten, but I do think it's good to understand what it is you're communicating. Even if what's being understood is not what you intended when you transmitted it, I think communication entails a responsibility for the speaker to consider the impact of their speech on the listener.
Completely honestly I'm a bit bewildered by your bewilderment. While it's obviously a huge, toxic rabbit hole and I don't really want to go there, I think perhaps you're not appreciating that people have genuine sensitivities about things you presumably don't. Maybe if I put it like this: There are contexts in which "toxic masculinity" or "fundamentalist Christians" aren't going to land well, and some people spend a lot of time in those contexts.