I care because, as a rational agent (or at least someone who aims to be), group-think affects me negatively when the group develops a dominant ideology which risks to infringe on my personal rights or take away opportunities from me sooner or later. I also believe that these dominant ideologies are harmful to the group and most of its honest/rational members.

It's important that members of the group keep an open mind so that the group doesn't become dogmatic. That's why I try to make contrarian arguments.