The older ones were symmetrical but always had the sides marked. Newer ones for Ai etc may be different. The crank you are supposed to detatch for service has changed between l&r over time too.
The spindle shouldn't wear if the bearings are kept good. If wear is suspected on either side, replace the spindle rather than turning it to swap l/r. Safety first or not at all!
——-new info
I found a spindle in my box and of course, it isn’t symmetrical at all. One side has a lip to maintain the position and meaning that the spindle can only be inserted/removed from that one side. If you are happy to swap this around and have measured the protrusion is the same on both sides and won’t change your chainline, then of course it’s OK. But some of the special spindles, like the one for the SRM powermeter, needed to be the right way round.