Of course they can have cold hearts. It's acceptable and even desirable for them, because they care so much more about humanity than the rest of us.
I was brought up to believe that Democrats/leftists really care about people, and Republicans/the right hate people. The left's unwavering support for abortion for any reason at any time made me doubt that premise.
If you actually go read through Republican Party history, it turns out that, with all their blunders, on average they have still shown up on the side of the angels far more often than their Democrat rivals. The thing is, the Elephant Party doesn’t like to trumpet it (please excuse the lame pun). So the braying Jackass Party steals the publicity. Modern liberals’ “love” is a cheap caricature of the true thing.
Many Libs view the world thru their ideology and don’t see people as individuals, but as members of groups. This permits all kinds of horrors to be perpetrated on the individual.