Nihilism is the belief that all values are baseless and that nothing can be known or communicated. It is often associated with extreme pessimism and a radical skepticism that condemns existence. A true nihilist would believe in nothing, have no loyalties, and no purpose other than, perhaps, an impulse to destroy.

Is it OK to be nihilistic?

You are right to reject it: nihilism is harmful and mistaken. However, it is not an abstruse philosophical irrelevance, because everyone falls into nihilism at least occasionally. I'll suggest that you may be more nihilistic than you realize, and it may be causing you more trouble than you think.

Do nihilists care about anything?

Nihilism does not imply that "one does not care about anything". For that can fit into another definition : Apatheism (although apatheism means one does not care about God's existence or non-existence). Anyway, Nihilists like any other philosophers, do actually care about purpose (or, in this case non-purpose).