Unfortunately, this is true. Studies have shown that White people generally have less empathy toward Black people, although there is a lot of individual variability. Moreover, individual variability correlated with implicit bias as measured by response time in congruence task tests similar to those featured in the Harvard Project Implicit.

https://implicit.harvard.edu/implicit/takeatest.html

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3108582/

Some people say that this is an innate genetic defect in people of European descent, but i don't think so. If you think about genetics, it doesn't make sense because race is a phenotype determined by a few superficial physical traits, while empathy depends on a great many social factors as cited in the above article.

More likely, it's in the way we're socialized, from very early on. That is, White people who didn't grow up around any Black people, who don't have any Black friends, neighbors, coworkers, or relatives, who get all their information about Black people from the media rather than from direct social contact, these tend to be less emphatic toward Black people than are White people who have had these direct face to face relations with Black people.

If empathy and race were in a direct cause and effect type of relation, there would not be so much individual variability correlated with social factors as noted above. This is why bigots violently opposed integration of public spaces during the mid 20th century civil rights struggles, and continue to oppose to this very day. This lack of empathy then supports the bad social policies which make for racism.

This correlation with social factors offers hope that we can close the empathy gap by changing the way we do things. That means, recognizing racism as a systemic problem in our society, and addressing it as such.