It's completely appropriate to have an identity crisis if/when there are honest fundamental disagreements.
I'm not sure that's the case here. Seems to me what's happened is that the antiwar lobby misconstrued the meaning of "neo-conservative", decided they could use it to slander pro-war people because it sounds sinister, and following this a lot of anti-war conservatives bought into it.
Now we get the spectacle of seeing each and every anti-war conservative spout off about what "their" personal definition of "neocon" is. It's embarrassing, but I'm not sure it's a big fundamental split here. Articles like the above may be able to make some headway in clearing up the mis-labelling that has taken place. I can hope...