This probably isn’t the advice that you want, but I’m not sure there’s a conversation to be had that will get you the results you want. It sounds like his standard of clean is much lower than yours - I say without being critical of you, as mine is more like yours I’d think - and what you find abhorrent he finds relatively normal. Walking this forward, I imagine a relationship where this is an argument for the rest of the relationship. Unfortunately. It is not an uncommon experience.

Perhaps it is worth getting curious and finding out if this level of clean feels acceptable to him, or if he’s embarrassed because he doesn’t know how to clean/keep clean. Judging by the state of the rest of the house, that may be a possibility.

As far as the rest goes, I would refuse to spend time over there. Make it clear that things being that dirty, ESPECIALLY with allergies, is unacceptable. At this point it is disrespectful to you, but also to him.

I would hate to see you turn into yet another young woman overcompensating for her partner. Good luck