While I would agree you don't really need to know or worry much about mathematical foundationalism to grok machine learning, anyone writing graduate level papers is going to understand some set theory since probability theory relies upon it. Even just the high school treatment tends to start out with intuitive visualizations of univariate discrete probability like defining a probability as the cardinality of an event space divided by the cardinality of a sample space, defining conjunction and disjunction as set intersection or set union of event spaces, defining mutual exclusivity as disjoint event spaces, and so on.

That said, there is probably no reason for anyone to dig too deep into theory without understanding why it matters first. And I don't think it ever matters if you're just trying to solve a problem with ML. Even if you want to overlay a solution on an image of a Sudoku puzzle, you don't need to understand why a particular algorithm works in order to be able to use it. Theory only matters if you're either trying to formally prove something works or possibly to guide you down more productive research paths in developing new algorithms, though honestly I'm not even sure that's really true any more. Just gaining a ton of experience with various possible techniques might generate intuition that is as useful or even more useful than actually understanding anything.

I almost hate saying that, as I have a deep personal love of math theory and think it is worth studying to me at least for its own sake, but this is sort of in the vein of whoever invented the curveball almost certainly didn't know much about aerodynamics and didn't need to. Discovering something does work may happen decades or even centuries before anyone figures out why it works.