You have got it completely wrong.
Believing in Karma does not mean behaving callously towards anyone who is suffering in any way.
It means being always kind, considerate and helpful towards those suffering.
By behaving callously, we ourselves would be incurring bad Karma.
And we never know when our own past Karma is going to strike us.
A person perfect, healthy and happy in every way can suddenly have a stroke or sclerosis.
Yes, everyone get the consequences of Karma, good and bad, there is no escape.
Of course in real life, everyone acts differently towards those suffering, whether they believe in Karma or not.
I repeat:
Karma and Reincarnation go together, as defined by those who explained these concepts thousands of years ago in India.
They do not make sense in isolation.
People in the West have learned the word Karma, but most don't understand what it really means.