The fact is, Arnold did what he had to do to become a world champion bodybuilder, first. Does sucking a dick give you bigger muscles? I don't know. But you could not deny that he was the best in the world. Do you think one of his contemporaries would be awarded Mr. O just because he sucked some dick or something? Ridiculous. Arnold was the best in the world and dominated.
Joe W. capitalized on that. I'm sure they both benefited tremendously. Works for Joe, works for Arnold.
Now in the mid-late 1970's, Arnold is relatively famous. He has a very large following, but not really outside of the bodybuilding world. But that large following is what gave Hollywood the willingness to take a bet on him. You can see the scene in Pumping Iron where Arnold and Joe are talking with the Hollywood agent, and the agent says "what you have going for you is your bodybuilding followers". There would be enough bodybuilder fans who would buy a ticket to make it worth Hollywood's $ risk. That's all. And Arnold was able to take that ball and run with it, and give the people what they wanted in action flicks. More and more money. He knew he could do it all along.
And next since he's an international movie star, he certainly has the popularity to become governor.
Step by step, that's all. He never could have made it into movies if he wasn't a world famous bodybuilder in the first place, meaning he had a built in audience. People flocked to him and that was good enough for Hollywood.