“This is even before getting to the problems with why she cannot convert. Even if you assume she could convert in the future, no one disputes as long as she’s not Jewish that he’s absolutely forbidden to be with her for even one more day.”
She can convert. All major batei din in North America, charedi and RCA included, convert people under these circumstances (a non-Jew married to a Jew). The kind of kiruv you’re advocating is just not the kind of kiruv that is actually practiced.
Yes, it is a sin to live with her, but becoming frum is a slow process, and rabbis counseling BTs have learned from experience (and da’as Torah) not to demand they change everything at once and stop all aveiros immediately. It’s also a grave sin every Shabbos he doesn’t observe properly. No one advocates going from 100% desecrating Shabbos to 100% observing Shabbos in one week — it simply isn’t possible without burning someone out.
“With a non-religious you should insist that she at least keep the bare minimum taharas hamishpacha.”
So the moment he realizes the Torah is true, he should leave her unless she immediately starts going to the mikvah and stops passing him things while she’s niddah? Sometimes it takes a few months for her to come around. If people acted according to your advice there would be so many unnecessarily broken homes.