Good ideas from several people. Best of luck sorting out this problem. The reality is that some caregivers are imperialistic about lifestyle choices--not just music but clothes and food, newspaper, TV channels. Quite unacceptable and you don't need to put up with it. You can find your voice on this matter, I'm sure of it. Be patient with yourself while you work up the nerve to challenge their behaviour.

What seems a reasonable position to take: It's your home, your life, therefore your music. When the carers are off duty they can listen to their choice in music. It wouldn't be the first time someone heard music they didn't love in the workplace. Life's like that. Where they can fairly expect you to give in is if you play music at harmful decibel levels--the carers are entitled to a safe workplace.

Later, after they accept whose home it is and that you are entitled to enjoy your own tastes without criticism, you can decide whether you'll deign to play music of their tastes from time to time.

If these so-called "carers" truly cannot grasp that you are entitled to listen to what you want (at more or less any age, in your own home), AND if someone else talking to them also doesn't help, why not go for a more Pavlovian approach? Be sullen, cranky and unco-operative (but not outright rude) EVERY time they criticize your music or insist on playing the stuff that leaves you cold. And when your own music is playing, be nice, compliment their hair, ask how their kids are doing, you get the idea. They'll soon realize their working life is a lot more pleasant if they play your music.

Actually one other option, if applicable, to try before you apply Pavlov is to speak with their supervisor at the agency that placed them. That's if they are from an agency or organization of some sort, and that you didn't put an ad in the paper and hire individuals out of the blue. If you didn't go through an agency, it's more work but if other remedies fail, it IS okay to fire them. I know of several people with various home care providers coming in, and it nearly always took several tries to get the best fit.