There was a problem with instaflate cans for cars, where people would go get their tire fixed and the mechanic would be smoking, unaware that the tire was filled with flammable gas.
Propane compatability with rubber is a good question. With instaflate, it is made for short term use. If propane has been used for a while for this application, then its probably ok.
I could see a very slight chance of hitting a rock, causing a spark with the rim, and your tubeless tire to come off the rim at the same time.
Or maybe even rubbing of spoke nipple with rim causing a spark. In these cases, a tube would be safer than tubeless.
The spoke nipple thing wouldn't be a problem if the tire was filed with propane only. It needs oxygen to make a flammable mixture. But there probably would be some oxygen in the tire before you started inflating with propane.
Other than that, awareness of the propane and taking precautions when doing maintenance (proper venting and purging before using tools, no smoking, etc), would be advised.