I tend to agree with your theory to an extent, as I do think fear is a major part, especially the fear of physical danger from getting "too deep".
However.. Ultimately I think that manifests in a lack of care that people care not enough for others and too much for their own comfort and well being. And this is I think a tactic used since perhaps the beginning of recorded history.. To scare the people or threaten them into not doing anything. If Jesus was a real person I think he was trying to teach us to not fear death, that we are eternal and if people really took that lesson to its depths then the people in power would have a much more difficult time controlling things and destroying/raping things!

However, even if people don't give a fuck in general or they don't give "much" of a fuck.. Then I still think we can help educate them or remind them or inspire them to care more in certain ways. I don't think all is lost even if the majority of the people seem to have lost most of their compassion for others outside of their immediate circle of close friends and family.