Should people who are economically center / left but socially ambivalent or conservative have a place in the coalition?

By this I mean "no war but class war" leftists who advocate for dropping minority rights to win back the working class, as well as former centrist liberals who say they will come back if the Dems "stop DEI" and things like that.

Both of these seem to be a fairly common views. After the Callais I saw a large percentage of leftists saying that Democrats caring about maximizing Black voter power specifically more than the general left is a demonstration of why they keep losing because they prioritize identity over policy. And I also see frequently from self identified liberals that Harris was a "DEI candidate" and that Democrats should go back to running white men and abandon their "anti-male" and "anti-white" policies if they want to win back the public.

To clarify I do not think that Harris was a DEI hire or that Democrats hate white men currently. But do people who do think this and demand that these be "fixed" have a place in our coalition?