The problem with Schwarzenegger is that he lives in two worlds: the progressive Hollywood world and the Republican politician world. I think personally he probably supports gay marriage, but he's a Republican. If he wants to advance his political career (as a Republican at least) he has to oppose gay marriage or at least not actively promote it. This is why the Republican party needs to divorce itself from the social conservatives. Arnold is really a Barry Goldwater style Republican, but he has to carry water for the social conservatives in order to stay respected in Republican circles.
Actually I don't think he supported Prop 8 (see hxxp://www.news10.net/news/local/story.aspx?storyid=50304). I seem to remember after the court decision came down allowing gay marriage, that he said he would not support or get involved with any attempts to amend the California constitution to outlaw gay marriage. I think he figured since the court made the decision he was home free: his fellow Republicans couldn't blame him for allowing gay marriage in California, but he also got to take credit among supporters of gay rights for not opposing the court decision. Prop 8 passing is probably a bit of a nightmare for him actually. A lot of angry people are going to remember his inaction and lukewarm support for the gay marriage efforts and vote accordingly next time he's up for reelection. That's why he wants the Supreme Court to overturn it.