Indonesia is a Muslim-majority country. There should be no non-Muslims running for a governor position in the first place. Imam An-Nawawi in his Sharh said:
قال القاضي عياض أجمع العلماء على أن الإمامة لا تنعقد لكافر وعلى أنه لو طرأ عليه الكفر انعزل قال وكذا لو ترك إقامة الصلوات والدعاء إليها قال وكذلك عند جمهورهم البدعة
NOTE. My own translation, so treat with care.
Qadi 'Ayyād said that there is an agreement among scholars that leadership is not to be given to a disbeliever, and [if given to a Muslim] if he shows signs of disbelief, he gets removed [from leadership]. He said that it is the same if he abandons prayers and calling for prayers, and for the majority of scholars this includes innovators [in religion].
— Sahih Muslim bi sharh al-Nawawi, Vol. 12, pp. 229 (Arabic only)
Ibn al-Mundhir was quoted saying the same ruling exactly in Ahkām Ahl al-Dhimma 2/787 (Arabic only) by Ibn Qayyim al-Jawziyya.
Those who are voting need to observe the criteria required in a leader in the Muslim world, and the first criterion is Islam. The majority of the scholars agree that this is based on:
وَلَن يَجْعَلَ اللَّهُ لِلْكَافِرِينَ عَلَى الْمُؤْمِنِينَ سَبِيلًا
and never will Allah give the disbelievers over the believers a way [to overcome them].
— Surat An-Nisa 4:141
I am not sure how you came to know that the Muslim governor is "planning to steal people's money." This is speculation that we are commanded not to do:
يَا أَيُّهَا الَّذِينَ آمَنُوا اجْتَنِبُوا كَثِيرًا مِّنَ الظَّنِّ إِنَّ بَعْضَ الظَّنِّ إِثْمٌ ۖ وَلَا تَجَسَّسُوا وَلَا يَغْتَب بَّعْضُكُم بَعْضًا ۚ أَيُحِبُّ أَحَدُكُمْ أَن يَأْكُلَ لَحْمَ أَخِيهِ مَيْتًا فَكَرِهْتُمُوهُ ۚ وَاتَّقُوا اللَّهَ ۚ إِنَّ اللَّهَ تَوَّابٌ رَّحِيمٌ
O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allah ; indeed, Allah is Accepting of repentance and Merciful.
— Surat Al-Hujurat 49:12
Assuming that the statement you made is accurate, and that the Muslim running for governor is planning to steal people's money, then look for another Muslim leader who does not plan on stealing people's money. This should not be a difficult task considering that premonition is obviously used in deciding whom to vote for.
You may refer to Islam Q&A's article "Is it permissible to swear allegiance to a kaafir ruler?" for more information.