sung by Dick Hogan https://www.youtube.com/watch?v=yX4XY1sqesc

In hard hats of labourers, red signifies danger or fire
https://www.color-meanings.com/hard-hat-color-codes-meanings/
I don't know whether or not that has any bearing on the song.

In the song the people with the red hats are the moneyed class
There is a symbolism of red hats for high society, but usually for women, I think. I am trying to find a historical reference rather than the social group for women, The Red Hat Society founded late 20th c., which is mainly what comes up if I do a search for the likes of "high society red hat". This strikes me as something Martin Ryan may have some information about.

British militia had red coats, were called redcoats. That doesn't get us any closer to red hats. The "Union" in the song lyrics would refer to the workhouse for indigent people.

Well, I think I'd better leave the "red hat" question to others now.