of course NO you can't use a present verb and a verb to be at the same time! you should say "don't you care anymore?" or "do you still care'

As a rule you can't combine between the auxiliary verb ( to do) and the verb (to be) in all forms of a sentence ,whether positive ,negative or interrogative.

"Are you don't care anymore?" Re-writing the sentence is the best solution. "Do you not care anymore?"

@ The above comment, that is very cruel and unnecessary. You should be ashamed of yourself.

Hi, this is a negative question... so as the other members have already stated we can't say, "Are you don't care anymore?" instead we would just use the basic structure of auxiliary verb + n’t + subject… In this case : Do (auxillary verb) n't you (subject) care (verb) anymore? Take Care :)