Why wouldn't working class whites vote for the Labor Party?
Presumably the ALP would have the same problems you described on your Appalachia thread. (Alienating working class whites with guns/religion comments). Or did you imagine them being more gun/pro-life friendly?
I would assume they'd be neutral. IIRC there was some discussion of the AFL-CIO adopting a pro-choice resolution in the 1990s (at the height of its reform period after Sweeney took over) that never saw the light of day because of the issues that come with that. Isn't the NDP a broad church as far as gun rights are concerned? One would think an American Labor Party would be. Bernie Sanders has a relatively pro-gun voting record, iirc