I was going to say that I agree, but that the party of the governor was a dependent variable on the state's overall political makeup...
...but then I recognize that California has had plenty of Republican governors going all the way back before Reagan, and California has [my entire life] been seen as a pretty left-wing whackadoodle state. During the period I lived here, we had the Governator, and I don't think that made the rest of the country think any differently of California--and certainly not any more highly lol...
It's true that California has had several Republican governors, but all--even Nixon and Reagan--were considered fairly moderate when they were elected (and Nixon and Reagan were a long time ago by political standards). Nowadays, a Republican's only shot at state-wide office is if people get really upset about taxes and there is a scandal involving the democratic incumbent, both of which led to the Governator.
The Governator was the last (likely for a while yet), but also a special circumstance. He won election through a recall, not the traditional primary system. He likely couldn't have won the Republican primary in California because when it happened the California Republican party was already too conservative for someone like him who was/is pro choice, tolerant of gay rights, and pro environmental protections. However, he took advantage of Gray Davis's unpopularity when the energy crisis hit, sticking the state with rolling blackouts and huge bills for overpriced power (to be fair, part of the state's financial troubles stemmed from giving away the store to the state's public employees' unions); ironically, the result of deregulation (of sorts) of the power grid. When Davis raised taxes and fees to deal with the financial trouble, that compounded the blackouts the state had been dealing with, and cost him his base of support, immediately after he was re-elected. A charismatic, middle-of-the-road, wealthy (largely self-funded), well-known celebrity was able to take advantage and was elected because (1) Davis was recalled; and (2) he didn't have to win a primary to get there.
Politically, Schwarzenegger was probably a fine fit for California, but at the micro level, he was known for trying to make everyone happy, which resulted in milquetoast policies that didn't demonstrably move the ball enough for anyone to really like him when he left office (his popularity was 1% point above Davis's when Davis was recalled).
