Using starting fluid typically only presents issues when starting 2-stroke and some diesel engines. In the former, it can cause lack of lubrication as the ether (a solvent) displaces or dilutes the gas/oil mixture. For the latter, it can cause pre-ignition due to the higher compression and ether does not play well with glow plugs and grid heaters.
In gas or propane OPE engines, it's safe to use.
FWIW, I have a gas/propane generator that starts on propane in all conditions. The same can be said for the half dozen propane forklifts at my work. I have heard stories from many folks that have trouble starting engines converted to propane (that were previously gasoline only), but in my experience, the ones equipped to run on propane from the factory start reasonably well even in the cold.