I started listening to the debate that the OP posted a couple of pages back, as well as a shorter Tom Holland interview, which is where I think the OP is drawing heavy inspiration from (he too uses the "swim in the waters" turn of phrase).
He (an atheist) is essentially arguing that Christianity's advent was the pivotal moment in shaping Western moral values and discourse, going forwards, to the extent that even non-Christians' moral analysis is rooted in Christian values.
In its most basic, I think that he's essentially saying that concepts of universal human rights are borne from Judeo Christian philosophy.
I do think Christianity helped develop and popularise that notion (which is a departure from the Roman culture then prevelant) and it is certainly quite possible that, absent Christianity, European moral views may have turned out quite differently.
That said, I do think there were suggestions/flickers (say, Stoicism, or the Cyrus Cylinder) that discourse concerning morality was heading in that direction.
Of course, I do think that for much of Christianity's history, it has failed quite spectacularly to live up to these purported ideals, and I think its trite to say that, since Christianity played a big role in developing and popularising the notion of equality, that all subsequent moral discourse is inherently Christian to an extent. If that's the position we are to accept, then I think the OP would have to concede that things she does not like (seemingly, euthanasia and gender-affirming care) are also rooted in Christianity.