If I were a superhero, I would probably have found myself in Spider-Man's shoes. In theory, I'm in favor of superhuman registration, but it has to be executed properly, and the government isn't going to do it perfectly. I'd recognize this, and accept the way it plays out because I know there is no perfect solution (I always find it funny when some group or another works against some bill that promotes their own cause just because it isn't perfect ... guess what, "perfect" is impossible in just about everything, especially in legislation). But when it came down to fighting other heroes, I would know I was on the wrong side.
For one, the anti-registration side is standing up for the very idea of superheroes, and as a superhero, that has to mean something to me. And secondly, as Reed has pointed out, Steve Rogers is probably the one man in 616 whose judgment I would trust implicitly. He doesn't have the arrogance of Xavier or Stark, or the hyperopia of Reed Richards (Reed's heart is always in the right place, but he often loses sight of what's in front of him by being distracted by the horizon).
As I was reading Civil War, the moment I instantly knew I was on Cap's side was when he jumped out of the helicarrier. Dude's got balls.
Interestingly, having read halfway through 1966 in the CMRO, the one person in the Silver Age I would say is the best leader is Nick Fury. I can see how Captain America will grow into who he was by the Civil War, but in the Silver Age he is very unsure of himself and is very easily drawn into squabbles with Hawkeye and Quicksilver. Sure he's a great tactical leader, but so is Fury, Summers, Richards, etc.