There's a difference between being required to be connected to the server because it's a multiplayer game, and being required to be connected to the server if it's a single player game.
If your game is multiplayer, it's fine for you to require people to be connected to your server (and then it's easy to do authentication, which is a very non-intrusive form of DRM). That makes sense. You can't do multiplayer networking if they aren't connected to the server in the first place, so that's fine.
If your game is single player, it makes little sense for you to require people to be connected to your server (which is a form of intrusive DRM).
Generally, people don't mind non-intrusive DRM that works. If your DRM is intrusive, or if it doesn't work*, people typically have issues with that.
So what should you do? Whatever makes sense. Just be logical and realistic in your decision making. Too many people/companies aren't.
*by works/doesn't work, I mean your DRM works if it lets legal customers play the game, and it doesn't work if it doesn't let legal customers play the game.