In short, yes a muslim can vote for a non muslim governor/president.
For a detailed answer continue to read:
The answer here would depend on many factors I'd say.
Now, in your case it seems you live in a muslim majority country (Indonesia). So that would be a very hugh factor in the answer. But I am not going to answer in according to that, because I do not live there and I don't know many important factors that is needed for an answer.
My answer will be more general speaking: can you vote for a non muslim, in a country which is not a muslim majority country? Because that makes it easier to answer.
My answer will be based on this: In a country where there are few muslims, 1 - 10%, how should one vote? Can one vote for a non muslim president?
First we must look at the variables:
- Are there even muslim candidates?
- If there are, do they even got a chance? (Consider the muslim population of 1 - 10%, and not all muslims voting one them, their chances must be very small.)
- Are there other parties that somehow can make life "harder" for muslims or other minorities?
- Are there parties that are "normal parties", with democratic values, equally treat all "groups" in the country the same and do not disparage any minorities?
Say, there are no muslim candidates, should I vote?
It depends, if it really doesn't matter on who you vote on, it's your choice to vote or not. If you think you might vote on a party that is good and you really feel that they would not make any indirect harm, then do that! There might be difference of opinions about this scenario.
Let say there are no muslim candidates, and there is a racist partiy or party that really might make life harder for muslim and other miniorites, then you should (or must) vote on the "normal party", which stands for democratic values and treat all as equal. Because if you don't do that, the racist party will earn a higher vote rate, even though you don't vote at all. And if they win, you will be indirectly a reason why life becomes harder for muslims/other miniorites.
Now, in the same situation as in scenario 2, EVEN THOUGH there are muslim candidates, you should still vote on the other party. Because, wasting your vote on the muslim candidate when they have no chance of winning (because the small number of muslims), will still make the racist party earn a higher vote rate (because the other parties loses your vote). So giving your vote to the other (non muslim, with deomcratic, and equal values) party, their vote rate will get higher, and at the same time the racist party's vote rate will become lower.
So, as I said, everything depends. All situations are different. One should try to look for best of the future. Only God knows the future, but that doesn't mean you should ignore all signs that might be telling where the future is heading.
I could even say, that even in a muslim majority country, one might vote for a non muslim. But as I have stated, all actions are based on many variables, where you try to make the world a better place and avoiding Fitna.