Rambam writes in Hilchos Melachim 8Hilchos Melachim 8:10 that Moshe Rabeinu commanded us to force all humans to follow the 7 Mitzvos (and if they refuse, we must execute them).
It is quite clear that in our times we don't have the power to enforce the penalty, but that doesn't mean that we are less obligated in trying to convince all people to follow the 7 Mitzvos voluntarily.
Some would argue that this obligates Jews to actively promote observance of the 7 laws among gentiles. Others would argue that although this is theoretically true, as a matter of priorities we should expend such energies on Jewish outreach first. But I can't imagine a justification for "not caring". It is quite clear that G-d cares so obviously we should care.