I think this is bait because it's the sort of thinking that 'feels right' without thinking too hard about it.
Not true. Right idea of family valuea is not about empathy and does not have much elements of empathy. It is more about establishing hierarchy and punishing you if you step put of it.
It is not even like they would be more emphatic toward disabled close ones. They dont extend empathy toward abused or sexually harassed female familly member or kid. Or to gay familly member.
Inward focus of the right is toward the members of they political and social group.
> left expresses more empathy to those outside their immediate circles (caring for the planet)
Left do cares more about planet, but also toward close ones that need help. A lot of leftist activism is motivated by personal experiences and experiences of close ones.
From a biological/evolutionary standpoint, that's the correct approach. Anything that reduces - chances at - reproduction or makes the population less fit is an issue that makes said population tend toward extinction.
I believe the science disagrees on this point. In the case of humans, adaptations that contributed most to our success as a species are a constellation of pro-social traits that enabled us to cooperate in organized fashion in relatively large numbers (which empathy plays a major role in mediating).
Evolutionary fitness is not always meaningful at the level of the individual, particularly in social animals. IIRC, there are a number of species in which individually-disadvantageous (i.e. purely altruistic) behaviors are conserved, despite their apparent adverse effects on individual fitness.
And we see it playing out globally: as groups become more socially conscious (aka "woke"), their TFR decreases. Just look at a world map showing TFR, and overlay that on one showing "wokeness" by nation. European nations are generally the most woke in the world, and have a generally low TFR. African nations are generally the least woke in the world, and have a comparatively high TFR.