There's a problem that if you care, as an average person, it's hard to do much with it. Every few years you can vote left or right, which unless you happen to live in a marginal constituency or swing state, has no effect.
>he Democratic party is left of center on social issues, even compared to Europe.
Actually, the Democratic Party is mostly libertarian (or classically liberal, if you like, which is, inherently right wing) on social issues -- preferring to allow people to make their own choices WRT their bodies rather than seeking government control of reproductive health and other forms of bodily autonomy.
Individual rights and personal agency are not "left wing," except in the eyes of the authoritarian far right (or far left) who seek control over all else.
So no. The Democratic Party has a solidly center-right agenda/ideology -- no collectivism, individual rights not curtailed by the state, freedom of thought and religion, etc.
Despite what some folks may say, there are no Marxists in the US Democratic Party.
That's not to say that the Democratic Party is the ideal. Far from it. But to place them on the absolute "left" is ridiculous on its face.
It's only "left wing" as compared with the far right (read: evangelical christians, white nationalists, xenophobes, etc.) Republican Party who want to limit women's reproductive choices, force the religious doctrines of the Christian church down everyone's throats and spout xenophobic and long debunked genetic tropes related to melanin content.
Caring = caring to understand how the system works and how the incentives work for participants in it.
If I'm super generous I would guess maybe 0,1 percent of the population cares by that definition.