If you take a minecart from A to B with same height between departure and arrival : no problem.
If you take a minecart from A to B where A is bedrock level and B above ground (example) : no problem.
If you take a minecart from A to B where A is above ground and B is placed deeply enough (difference between blocks) that the drop would kill you : it DOES kill you to exit the minecart.
Death can be avoided by wearing diamond armor + featherfall boots.
Can't be recreated in solo mode, maybe a multiplayer plugin causing this or exclusive to server mode.