That depends on party registration and political philosophy. For Democrats and liberals it probably isn't.
Until 1984, anyone holding dual citizenship could not run for Governor of California. That was just 20 years ago.
Sworn, divided political allegiance was felt intolerable by our founding fathers and that abomination is near the top of my list of unspeakable crimes for a political party to commit. Especially a party which has traditionally prided itself in upholding original intent and founding principles. The only justifiable desertion by the GOP, in the mid 19th century, that I can recall, was the 3/5s rule.
That's nonsense. Historically the state of California has always had a low eligibility threshold with regard to both US citizenship and State residency. That's because the most of the original inhabitants favoring statehood were Mexican (or Californios as they preferred to be called), and assorted white settlers from all over the United States and Europe.
Since you're such a big fan of original intent, here is the section of the 1849 California State Constitution that deals with citizenship and residency
"Sec. 3: No person shall be eligible to the office of the Governor, (except at the first election) who has not been a citizen of the United States and a resident of this State two years next preceding the election, and attained the age of twenty-five years at the time of said election."
Not a word about barring those holding dual citizenship and for a very good reason.