Actually propane is not an uncommon refrigerant. It is also known as R290 in the refrigeration community. It has been used in air conditioners, space heaters, refrigerators, and freezers. Even in some advanced countries in Europe and Asia. Why they allow this? I don't really know.
Also, they don't use oxygen for pressure testing. They use nitrogen, a cheap, non reactive, and heavy gas, ideal for pressure testing.
Why the Indian Navy decided to use propane in the AC of a warship? Only they know. My guess is that since propane is one of the cheapest AC Freons. They went for the cheapest option.