Well, if he had a more successful film career, it is not outside the realm of possibility for one of the two major parties to approach him to run for something in California. Rumors that a celebrity might run for high office there have popped up for decades, though relatively few of them actually go through with it (and my impression is that the ones who do, and went on to win, such as George Murphy, Ronald Reagan, Sony Bono, Clint Eastwood, and Arnold Schwarzenegger, seem disproportionately Republican for whatever reason).
That said, unlike Ronald Reagan or John Wayne on the right, or any number of left-wing celebrities, I do not know that Audie Murphy ever expressed any strong political views publicly.