Yes if you are of different religions even as Indonesians you may marry in Thailand

As for your paperwork :
There are papers you must bring from your home town.
  The Indo embassy will require the paperwork to be complete and will take their time to process it minium of ten days form handing the papers to the embassy till they return.

• Original and copy of ID Card (KTP)
• Original and copy of passport
• Elucidation of marital status from District office in Indonesia (Surat Keterangan Belum Menikah dari Kelurahan/Kecamatan)
• Original of Divorce Certificate (for divorce status)
• Original and copy of Death Certificate of ex husband/wife (for widow/widower)
• Parent permission letter legalized by District Office (for the one who are under 20 years old){if your under twenty it will be much harder so let me know ahead of time}
  
• Administration fees: US$ 20 (payment only in US dollar)
• Application must be made in person
• The above documents need not to be translated in English
• Application time is at 09.00-11.45 of every working days. The document will be returned on the next working days at 14.00-15.30
  

This is what past couples required but you MUST check with them for current requirements!!!

http://www.kbri-bangkok.com/

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