You have a right to vote, an obligation to serve on a jury, etc. You have no right to fly on an airplane.
There is a big difference between the examples you provided and going to an airport to get on a flight provided by a private company to allow you to travel. It's no different than someone that has earned Diamond status on Delta and gets to board the plane early, get upgraded to first class or receive discounts to purchasing tickets. There are privileges to membership that people earn or buy and that is part of how our economy works.
There should not be a preferential system for elections or justice as those are specific rights that citizens of the US have been granted.