To give you anything other than a personal subjective response you'd first have to define "morality" and then "types of people" and explain how the two things are related.

My definition of morality is "the emergent and continually evolving consensus of society on what sustainably makes it more, rather than less, civil and fair". It is then up to each member of society to support that, or not. And if they don't support the moral consensus, to decide whether to rebel, or work within the system for change.

Conformance to morality is individual and all personality types or different subgroups really do is to add indirection to the process of social interactions that inform societal morality.

People who care about other people

'Type'?

I suppose the 'type' of person that cares about others as opposed to one that doesn't give a shit.

There is no answer. Morals are subjective and not just by regions or races or religions or sexes but down to the individual. That is also assuming that "morality" has a defined set of guidelines which it does not. The best response you'd get to defining morality would be majority rule.

The best answer I could provide is "not sociopaths or psychopaths".

I've heard that British Columbia has the best Morels

People who can recognize compassion and empathy.

You'll find the people with the best morals are those who share in your same moral values

Generally, those ones who'll bring up morality possess the worst.

Living ones.
The dead don't care.

Moral ones. Sorry but I don't see any over arching category of morality that applies to any demographic.