Could you please tell me if there are polite ways to say "What do I care?"/ "Why should I care?"

Hi Julia

Yes, they are usually considered abrupt, maybe even rude - it depends a lot on the tone of voice and the body language - you could just shrug your shoulders!

For the first, maybe "Sorry, I'm not interested in the slightest". or "I'm just not interested"
For the second, perhaps "It's nothing to do with me." or "It's no concern of mine"