Welcome to the board!
Thanks for asking such an easy question.
So, let's see. First, review the 49ers recent history. To cut a long story short they have gone from mediocre under a series of coaches (in an incredibly weak division) to a very, very good team under Harbaugh. What's more, he's done it in very little time using a lot of players who were a big disappointment under previous regimes. How can you not trust this guy to make decisions?
Second, is this a decision that fans can make? In many sports (and maybe some positions in this sport) you can watch players and make up your mind. But a quarterback is much more than the actual throws he makes -- that's just the end of the process. There's all of the information processing and decision-making that goes with it. We don't see that -- we just see the end result.
Third, changing is one of the most consequential and difficult things that any coach can do. The guy who is in position always has an incumbency advantage -- he knows the system from the inside, has taken the reps, in games and in practice. It's easy enough to come in like Andrew Luck when a team absolutely blows but at other times there are costs. It may even be that it makes SF an easier opponent on Sunday (though Kaepernick looked pretty useful to me against Chicago).
So it's dead simple -- if you guys aren't insane you will back whatever Harbaugh wants.