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Thailand DOES accept a US I-327 Re-Entry Permit in lieu of a passport, however you WILL require a visa in order to travel to Thailand using that document. On your return to the US, the US will obviously also accept the I-327 for re-entry.
You will also need to consider your route from the US to Thailand as not all countries will let you transit using only an I-327 - you may require a visa or may not be allowed transit at all through some countries.