"Judeo-Christian" as a favored ethnic group is a construct of postwar white supremacy, borne of the need to pretend white supremacy is not anti-Semitic. Before the Holocaust made overt anti-Semitism unacceptable in the Western world, the only people who talked about Judeo-Christian anything were a handful of intellectuals.
Somewhat tellingly, the US, which did favor Northern and Western Europe over Southern and Eastern Europe in its immigration law, passed an amendment establishing a separate quota for Jews to prevent German Jews from getting in using the generous German quota.
This is a harsh take, but the emergence of the inevitable 'the Mooslim alien menace' garbage from various usual suspects using the expression does make it seem accurate.
Eventually, Santamaria and the DLP (same thing at that point) was pushing against the White Australia policy when the hard Left unions were pandering to a weakened and still very racist Arthur Calwell.
I'm definitely not a fan of Santamaria, I think this was a case of him being inadvertently good; and I think Calwell's inability to voluntarily move towards a tolerant migration policy, plus his slide into an alliance with the execrable tankies, was a tragedy for an otherwise more credible politician.
Anyway, there are essentially no racially tolerant trade unions/unionists in the federation-era timeframe OPer is supposedly addressing. Billy Lane, remember, comrade.