i know it's drivel but I kind of want to answer the question seriously
Like you said, there's an image of the "working class" that entails a bunch of broad shouldered white guys who like beer and go to a Baptist church on Sunday. In reality it's every demographic and organizing the working class means organizing for universal issues. Even entertaining the example. Ok, they're about to go on strike and don't support gay marriage. Is step 2 after the strike is successful to go abolish gay marriage? Is that part of the platform of the iron union?
In reality the working class is diverse and complicated, united by the common aspect of being laborers. I've tried organizing before, nearly twice forming a union, and we had a few chuds lining up. They never really brought up their socially reactionary nonsense because they were A) outnumbered about 4 to 1 and B) they had awareness enough to know it would be disruptive, so the chud elements were immediately diluted out from the start. We didn't succeed in forming a union, but I can only imagine maintaining stability would become of even greater importance going forward. The chuds would have probably been even more scrutinized and more encouraged to fall in line, since their money, healthcare, etc would have been on the line if they made themselves poor examples of the union or were being disruptive with saying slurs or whatever.
Any wide working class organization in the USA that manages to get off the ground would have socially reactionary elements within it, but they would be vastly outnumbered simply by sheer virtue of who the working class comprises of.
Also, this is a wider concern, but what should leftists care what values a person has in their soul or whatever if they have no power to exercise those values? Ok so I've got a bunch of iron workers who don't like gay marriage or abortion. So the fuck what? Let them seethe and mumble under their breath how much they hate it as long as their organizational capacity gives them no power to unilaterally execute those values.