I can't think of any other high-profile professional sport where the fans can be so closely connected to the competitors. In golf, it's not just showing up to a stadium and watching a few uniformed men toss a ball around while you drink a few beers from a distance. You can follow the competitor around, listen to what they say, see how they react, etc. It's definitely touchy-feely sounding, but you can become more easily connected with a golfer than you can with any other athlete - even on a television screen.
For that reason, I think your attitude/appearance is more important in golf as far as fan reception or respect is concerned. Golfers can appear to be more "human" than other athletes. Before, his mannerisms were attributed to intensity, desire, and winning. Now, after all the womanizing, lying, etc., his mannerisms could easily be interpreted at him simply being a jerk-off. Like I mentioned, despite him being an incredible golfer, I was getting very tired of watching him slam clubs and look like he wanted to die half the time when he was on the course. Many will get past it and continue following him because he's an amazing golfer. But, there could just as well be a significant drop-off in his support should he continue being so stoic. The guy doesn't have anything to prove competitively any longer - he's done it all - we all know he's the best.
I'm not suggesting he should not take the game seriously...intensity/fire and appearing to enjoy what you do for a living don't have to be mutually exclusive.