Badiou first drew my attention to the Counter-Enlightenment concept of “antiphilosophy”. He uses this as a kind of spice, ostensibly to keep philosophy on its toes. I find it useful as a historical category, but apply it with different extension and different valuation. Jonathan Israel discusses the original Counter-Enlightenment version in Enlightenment Contested.
To me, antiphilosophy is unequivocally a bad thing. I take it to be defined by an overt or implicit hostility to philosophy as an integral discipline — or to most philosophy — while at the same time appropriating pieces of it. It is (I say with polemical voice) the pseudo-philosophy of people who actively refuse the rational discipline of real philosophy, but want to cherry-pick a few conclusions for a different agenda.
Consistent with that, I would not want to call Nietzsche or Wittgenstein or Lacan an antiphilosopher, as Badiou does. For me, the antiphilosophers include (paradigmatically) the voluntaristic, emphatically supernaturalist theologians like Philo of Alexandria or al-Ghazali who explicitly saw themselves in competition with “philosophy”; then the Counter-Enlightenment people who coined the word antiphilosophy; then also, other avowed antirationalists like Rousseau and Kierkegaard; those like Descartes who hold the history of philosophy in utter contempt; the cruder advocates of empiricism; and unfortunately many political leaders.