While watching the Banshee at https://www.youtube.com/watch?v=khVPlD2rNfc, which shows a ground crewman exiting on the right side. the question occurred to me—on which side of most top-entrance jet aircraft are built-in steps, left or right? And what about external, crew chief erected boarding ladders?
Which got me to thinking. It turns out that carrier-based propeller-driven fighters tended to have the boarding provisions on both sides of the fuselage, like the F6F Hellcat.
These big engines needed to be warmed up. This allowed a crew chief to do so if desired and then climb out of the cockpit on one side while the pilot climbed in from the other.
The F4U Corsair had a similar arrangement, but eventually the boarding provisions on the right side were somewhat more user friendly than the ones on the left, as with this F4U-5P that had a boarding step extending out from the fuselage.
The earliest jets were a mixed bag. The FH-1 had boarding steps on the right side but not on the left.
Note that there was a non-skid patch on the nose landing-gear door for the first step with the left foot.
The FJ-1 had boarding steps on both sides (there was also a door that opened on the left side as there was on the right).
Since boarding provisions were heavy and jets didn't need to be warmed up, my guess is that it was quickly determined that only access was required from only one side. But which side?
The F6U Pirate was boarded from the left side.
But the F3D was boarded from the right.
As was the XF2D-1 as Jack noted:
(Note that the landing gear door was not used as a step.)
However, the production F2H was boarded only from the left, with the gear door again serving for the first step.
The F9F Panther was also boarded from the left side, which was now standard.
There were only two exceptions to the self-board requirement. One was the A4D Skyhawk. Self-boarding was one of many things left off in the pursuit of minimum empty weight (also see http://thanlont.blogspot.com/2011/09/self-boarding-for-douglas-skyhawk.html). The other was the F4D Skyray. In the latter case, both the mockup and the prototypes featured self-boarding from the left side.
However, by the time the XF4D was ready for at-sea carrier qualification, it had more of a nose-up stance and a ladder (mounted on the left side) was needed to reach the cockpit.
Somehow Douglas convinced the Navy to forego F4D self-boarding, probably because its contemporary, the A4D, didn't have self-boarding and used a similar ladder, (different than the one shown above) that could be attached only to the left side of the fuselage.
Similarly, the F3H Demon, which was delivered with self-boarding capability (see http://thanlont.blogspot.com/2009/06/self-boarding.html for the XF3H and http://thanlont.blogspot.com/2008/05/i-had-hoped-to-find-picture-like-this.html for the F3H), was allowed to have ladders even aboard carriers as was the F7U-3, which probably avoided several broken bones or worse (note that the F7U-1 steps have become pegs with a giant step required from the engine nacelle to the first peg and another from the second peg to the cockpit).
Why access from the left side? My guess is that given the primitive fuel controls of the first jet engines, a pilot's first start or two during his initial checkout in jets needed to be demonstrated and/or closely monitored in order to avoid overtemping the engine. Since the throttle was on the left side of the cockpit, the instruction by an experienced pilot or crew chief needed to be from the left side of the airplane.