I think it’s pretty obvious that if the Democratic Party changed that drastically, the person you replied to would change their opinion. They are saying that because, at present, Republicans are far, far more dangerous.
Also, Democrats have been championing civil rights since JFK. Saying 1960 was not that long ago is silly. Suffering that 1866, which is when the poster you posted was made, is not that long ago when it comes to American politics is not even rational.