If you look closely at it, liberalism too is problematic. Much of modern thought is devoted to supporting humanism, liberalism, and secular views of morality, law, art, and so on. There's no guarantee this modern project will succeed. It arose as a revolution in Europe, as a synthesis of some ancient and medieval Christian ideas, and as a result of some scientistic discoveries.

If a skeptic challenges a secular humanist's conception of natural or inherent human rights, the humanist will face some problems. Yuval Harari points out that transhumanism, or radical advances in technology present other challenges to the humanist's self-image.

Conservatism is a lazy or defeatist reaction to modernity. Instead of running with the adventure, the conservative retreats, in effect, to premodern (anti-humanistic) and often savage, self-serving prejudices.

Anyway, that's just how I see it. We needn't trust absolutely in any philosophy, though. And much depends on how "conservatism" is defined. As I said, sometimes so-called conservatism is just old-school, early-modern liberalism. It gets confusing.