Is Haftar still considered the relatively culturally liberal/secular choice in Libya or have I fallen behind the news?
No, and he never was.
I mean, he is modestly secular by Libya standards, but he is absolutely not liberal by any stretch of the imagination.
Most of the world isn't liberal. In much of the world outside the West, the leftists would be considered socially conservative by our standards.
So, eastern Libya is economically conservative while western Libya is socially conservative?
No, I'm saying most of the world is socially conservative, and only "the West" is fairly socially liberal.
Social liberalism is not what "liberalism" means in this context, though. When we say Haftar is illiberal, we mean that he will likely not adhere to small-d democratic norms, that he represses freedom of expression and criticism, and that he will likely not seek to integrate Libya into the global community of nations.