My general take on this game:
It's in bad taste, it's simplistic, and kind of dull as a game, other than trying to gauge the depravity of your friends (which can be amusing). I've played it once.
Why is it popular? It's an artifact of our times. We're deeply attached to identity politics, how lacking much else, many people (especially young people, it's argued) have taken their self identities as concrete and irrefutable, looking for offense and hoping to pillory anyone who disagrees, whether it's a web article or a coffee shop that serves the wrong type of bagel.
We live in a culture of perpetual outrage, and increasing fear of giving offense. You can have your business or your job taken from you with the wrong tweet or when someone has been slighted by your employee. Lacking strong cultural ties, we make up new identity constructs, and man, do we grow attached to them. We not only spend all our time immersed in our new identities, but we take great offense when that identity is questioned. 20 years ago, Cards Against Humanity would have gone nowhere. It would have been simply, offensive.
It's popular because Cards Against Humanity offers up an evening of offensiveness as a way to step back from self identities and closely protected beliefs that are ultimately bullshit and empty of meaning. It's more a therapy tool than an actual game. Personally, I find that kind of boring, but if your life is a rigid, oppressive self identity paradigm, or you've been forced to live within one, it might let you take a step back, possibly providing some empty space to find some much needed humor.
Or maybe I'm entirely wrong and it's as bad as people say. Maybe I'm standing on a soapbox of privilege, defending an instrument of evil while the world burns. I can't decide.