What is the ruling on some people saying, when advised against a wrongdoing, "This is none of your business; mind your own affairs and do not interfere in my private matters"?

Their words are false and rejected. Allah detests such a response, and the proof for this is the authentic Hadith: "Indeed, the most beloved words to Allah for a servant to say are: 'Glory be to You, O Allah, and with Your praise, and blessed is Your Name, and exalted is Your Majesty, and there is no god besides You.' And the most detested words to Allah are for a man to say to another man: 'Fear Allah,' and he replies: 'Mind your own business.'" So, you must continue to call people to good and be patient, as Luqman said to his son: "O my son, establish prayer, enjoin what is right, forbid what is wrong, and be patient over what befalls you. Indeed, that is of the matters [requiring] determination."