Few today refer to the Democratic Party as the working man’s party. It’s more of a social justice party.
Who is few? You? This is a Trumpism ... someone is telling me .... yes the voices.
I believe Pres Biden routinely refers to the Democrat Party as the working class party i.e. the working man's party. What Republican legislation earns them the right to be called the working man's party? I suspect no legislation. Republicans (the one's who continue to believe in some political philosophy would say trickle down is the way to help the working man) routinely pass legislation which primarily helps businesses and the more wealthy folks. Whereas, Democrats routinely pass legislation which directly helps the working class folks.
Now, it is easy to say something which is not true, and to continue to say it, does not make it valid. That is the Trump approach to truth. If he lies enough and doubles down on the lie (yep it becomes the "big lie" for which Goebbels is so famous) the base will assuredly believe it.
Both aspects can be true and valid at the same time. The Republican Party does not represent either. You can believe their lie, but it doesn't make it true.
I rather suspect the changing demographics of parties has more to do with non-political characteristics, than political philosophy. Take a look at the changing allegiance of parties in the South following the CRA. Southern Democrats abandoned the Democrat party in favor of the minority Republican party for one reason only, and it has nothing to do with politics, and everything to do with bigotry (I know ... I know ... it can be considered a political statement). So can one argue the loss of Democrat base has anything to do with race? I don't know, but it raises the specter of the possibility the underlying polarization between people is based on bigotry and not politics. A possible argumentative point is consider what the Republican (read that Trump Party) tenets are. Whatever Trump says they are, and of course one could construe that to mean building a wall between peoples as the driving force of the current widening schism between parties and people. Consider the non-sensical position of Republicans to stand in favor of killing Americans by ignoring public health measures. Consider the long running indoctrination campaign conducted by right wing groups using Fox News as a lever to wedge peoples apart.
I think Dylan said it best ... "something is happening here but you don't know what it is
Do you, Mr. Jones?"