Yes, I’m not saying that we should tell people they must stay with their non-Jewish spouse. But we don’t demand they leave, even if they ask us what they should do — that’s up to the individual. Every BT does what they do on their own time, so why not, while they’re doing that, give the non-Jew a chance to decide is she wants to convert? In many cases she does, with all her heart. It makes sense, as much as anything makes sense in the messy process of becoming a BT.
“Same with a non-religious woman. Ideally he must stop living with her immediately. ”
Not according to Rav Arush in Garden of Peace. See it inside. No BT can demand his wife become a BT overnight or else. People have to be practical. No kiruv rabbi advocates radical overnight changes and demands for such of one’s spouse, because it’s counterproductive.
“Regarding conversion, Chareidi butei dinim absolutely do not convert intermarried spouses.”
This is not true. I know of cases myself in charedi batei din. In Israel there are authorities who forbid someone “married” to a non-Jew to convert (I think R’ Shternbuch is an example), but in the US it certainly happens. It is typical to require a period of symbolic separation (while still living in the same home) between the spouses as the gerus is finalized.
Interestingly, think of the case of the non-Jew married with two kids to a secular Jew, and the non-Jew on her own wants to convert. (This scenario is pretty common….) The only way for her and the kids to convert is if they stay together and he slowly becomes religious enough to make it happen! If she leaves him right away (which would be your advice always), she will never convert (and he will never make teshuvah), because the kids will be eating cheeseburgers with daddy every other week, when he has custody, and the beis din can’t convert kids like that in such a situation, and they can’t convert her if she has goyish kids who will be living with her. But if she bides her time and plays her cards right, within a few months or years, he’ll become religious enough and she and the kids can convert.