The debate goes on and on, what is a sport, what is not a sport. It is a question that will not be resolved, except that everyone should agree cheerleading is not a sport.
So what about the fans? If you attend a baseball game, from the majors down to kids t-ball you're a sports fan. You are there to watch the game, have a dog, and cheer for your team. Same for football. Basketball? All college b-ball fans are sports fans. At the NBA most folks are sports fans, some are not. The latter category includes celebrities who go to NBA games so they can get their picture in People magazine, or the NBA groupies who are there to get pregnant by a pro b-ball player (see also Shawn Kemp). They have little if any care (or at times, clue) what is going on during the game. (Boxing fans are the same as NBA fans, those in the first 2 rows aren't fans, the rest of the folks in attendance are true sports fans.)
Soccer fans are sports fans. In fact they may be the most devoted sports fans, not because they will brawl with anyone supporting the opposing team, but mainly because they are willing to sit and watch a game for hours even though neither team is likely to ever score. Soccer may be one of the most boring games ever invented (because of the lack of scoring) yet these fans stay excited. Soccer fans are definately sports fans.
Golf fans. Not really sports fans. I love golf, it is a great game to play and the most difficulut of all sports to master. I've also attended one U.S. Open (1992 at Pebble Beach) and 3 other pro teournies. Having done so I can attest to the fact that golf fans are not really sports fans for two reasons. First many of the people at the tourney are there mainly to network. They're either corp. hosts or guests, spending most of the time at the VIP tent or the souvenir shop, talking about business more than who's leading or who will win. Secondly, golf itself is not that great to watch in person. The player hits a shot and then moves on so you either see the whole pack play one hole or you watch a few players play the whole course. Either way you miss about 90% of the best shots.
Auto racing: Definately NOT sports fans. They turn out in great numbers to watch their favorites but the reality is their main motivation is to drink beer, chew tobacco (NASCAR), and hope to see a horrific crash. I can look out my office window and watch traffic on Interstate 80 to see much the same thing (except the cars aren't perpetually going around and around).
Pro Wrestling and MMA. First off pro wrestling is scripted so you aren't even watching a sport to begin with. Those fans are the same as musical theatre fans, except they have lower incomes. MMA fans aren't sports fans because they are not interested in a sport, they just want to see blood and excessive violence. As I noted above most boxing fans are sports fans, because they appreciate how much agility boxing requires. MMA is "professional" street-fighting, with kicks and chokes. These "fans" don't care about agility or sportmanship they, just want to see someone get the life beat out of them. Given the opportunity they would also attend a dog-fight and consider one dog killing another a sport.
The Olympics: Everyone who watches in person or on TV is a sports fan because every event (even sailing and shooting) are universally sports and the fan is there to witness and cheer great acheivement and effort.