I think the answer is not in caring less, but in caring more in a skilful way.
Let’s go back to the Sutta, I find MN8 is particularly inspiring for me as a new Dhamma student.
These 44 effacements in MN8 could be used as personal determinations. They have helped me along my path.
Effacement
“Now, Cunda, here effacement should be practised by you:
(1) ‘Others will be cruel; we shall not be cruel here’: effacement should be practised thus.
(2) ‘Others will kill living beings; we shall abstain from killing living beings here’: effacement should be practised thus.
(3) ‘Others will take what is not given; we shall abstain from taking what is not given here’: effacement should be practised thus.
(4) ‘Others will be uncelibate; we shall be celibate here’: effacement should be practised thus.
(5) ‘Others will speak falsehood; we shall abstain from false speech here’: effacement should be practised thus.
(6) ‘Others will speak maliciously; we shall abstain from malicious speech here’: effacement should be practised thus.
(7) ‘Others will speak harshly; we shall abstain from harsh speech here’: effacement should be practised thus.
(8) ‘Others will gossip; we shall abstain from gossip here’: effacement should be practised thus.
(9) ‘Others will be covetous; we shall be uncovetous here’: effacement should be practised thus.
(10) ‘Others will have ill will; we shall be without ill will here’: effacement should be practised thus.
(11) ‘Others will be of wrong view; we shall be of right view here’: effacement should be practised thus.
(12) ‘Others will be of wrong intention; we shall be of right intention here’: effacement should be practised thus.
(13) ‘Others will be of wrong speech; we shall be of right speech here’: effacement should be practised thus.
(14) ‘Others will be of wrong action; we shall be of right action here’: effacement should be practised thus.
(15) ‘Others will be of wrong livelihood; we shall be of right livelihood here’: effacement should be practised thus.
(16) ‘Others will be of wrong effort; we shall be of right effort here’: effacement should be practised thus.
(17) ‘Others will be of wrong mindfulness; we shall be of right mindfulness here’: effacement should be practised thus.
(18) ‘Others will be of wrong concentration; we shall be of right concentration here’: effacement should be practised thus.
(19) ‘Others will be of wrong knowledge; we shall be of right knowledge here’: effacement should be practised thus.
(20) ‘Others will be of wrong deliverance; we shall be of right deliverance here’: effacement should be practised thus.
(21) ‘Others will be overcome by sloth and torpor; we shall be free from sloth and torpor here’: effacement should be practised thus.
(22) ‘Others will be restless; we shall not be restless here’: effacement should be practised thus.
(23) ‘Others will be doubters; we shall go beyond doubt here’: effacement should be practised thus.
(24) ‘Others will be angry; we shall not be angry here’: effacement should be practised thus.
(25) ‘Others will be resentful; we shall not be resentful here’: effacement should be practised thus.
(26) ‘Others will be contemptuous; we shall not be contemptuous here’: effacement should be practised thus.
(27) ‘Others will be insolent; we shall not be insolent here’: effacement should be practised thus.
(28) ‘Others will be envious; we shall not be envious here’: effacement should be practised thus.
(29) ‘Others will be avaricious; we shall not be avaricious here’: effacement should be practised thus.
(30) ‘Others will be fraudulent; we shall not be fraudulent here’: effacement should be practised thus.
(31) ‘Others will be deceitful; we shall not be deceitful here’: effacement should be practised thus.
(32) ‘Others will be obstinate; we shall not be obstinate here’: effacement should be practised thus.
(33) ‘Others will be arrogant; we shall not be arrogant here’: effacement should be practised thus.
(34) ‘Others will be difficult to admonish; we shall be easy to admonish here’: effacement should be practised thus.
(35) ‘Others will have bad friends; we shall have good friends here’: effacement should be practised thus.
(36) ‘Others will be negligent; we shall be diligent here’: effacement should be practised thus.
(37) ‘Others will be faithless; we shall be faithful here’: effacement should be practised thus.
(38) ‘Others will be shameless; we shall be shameful here’: effacement should be practised thus.
(39) ‘Others will have no fear of wrongdoing; we shall be afraid of wrongdoing here’: effacement should be practised thus.
(40) ‘Others will be of little learning; we shall be of great learning here’: effacement should be practised thus.
(41) ‘Others will be lazy; we shall be energetic here’: effacement should be practised thus.
(42) ‘Others will be unmindful; we shall be established in mindfulness here’: effacement should be practised thus.
(43) ‘Others will lack wisdom; we shall possess wisdom here’: effacement should be practised thus.
(44) ‘Others will adhere to their own views, hold on to them tenaciously, and relinquish them with difficulty; we shall not adhere to our own views or hold on to them tenaciously, but shall relinquish them easily’: effacement should be practised thus.
When you focus on your own wholesome determination and action, you will find a lot of joy in what you have achieved. You will see that other people’s shortcomings will be their own business and you won’t be so consumed by that.
In short: we tend our own garden.
Also, please keep in mind the advice is applicable in a spiritual setting and for the cultivation of peace. You are dealing with the world, the mundane. Sutta have their limitation. We have to rely on our own wisdom about the world to solve the problem in its context.