For one, I find it damn funny even though most of the parts I laugh at aren't the clumsy broad laughs the film is aiming for. John Wayne isn't what I'd call a gifted comedian, but he'll occasionally find some wry humor in a line that you wouldn't expect to be there, or shoot someone a withering look that hits the mark square.
It also completely encapsulates why Wayne is such a conservative icon. McLintock is the archetypical captain of industry. He's built an empire out of little more than a tireless work ethic and incorruptible character. He puts justice and his own personal code of ethics over the law and civilized custom. And he has a deep and abiding love for the good old US of A. He's like an Ayn Rand hero, but with dialogue that actually sounds like it could have been plausibly uttered by a human being.
Of course he also lacks the necessary disdain for non-whites, college-educated young 'uns, and the environment to be a perfect modern Republican. But I doubt he'll be relegated to RINO status any time soon. Being a dead saint gets you a pass on those kinds of indiscretions.