While I admit this is pretty cute, this isn't canon by any means, so that's what makes it cringy. My opinion on AUs that make canon characters trans is that the better AUs are the ones where a male character wants to be female or vice versa, instead of a canon male character turning out to have been born female or vice versa, just because the former adds more to the story(the latter only affects backstories(and even then, always makes them cliche as fuck) and smut scenes). This whole idea of Luigi being trans isn't a "theory" or even a "headcanon." A headcanon is typically classified as a random, more minor detail that is plausible. A theory is typically much larger, and is based on serious evidence. This is really just an AU concept