What!? This is a matter of rational thinking. His parents provided no rational basis on why he has to do this particular activity on a regular basis. It's stupid tradition, and complaint is only reasonable, if not the only reaction favorable to the value of reason. 1st world or what has nothing to do with this. (Course, this just my hubristic interpretation of the motivations involved.)
If being nagged to make ones bed is a big enough problem in ones life to bitch about it publicly, then yeah, I am guessing it qualify's as a genuine First World Problem.
The rational basis is that s/he needs to learn cleanliness and orderliness in order to be more effective and or successful in ones endeavors in life, as well as an undertone of learning to be respectful towards others. Whether or not these things are valid completely can be disputed, whether there is a reasonable rationale behind them- not as easily disputed.
The parents have put hard work into making a home and they would like that home to be respected and seen as beautiful, asking one to make their bed and keep things tidy is not unreasonable at all when they are being given a home. If the OP is an adult who pulls their own fair share of the weight, including paying their own way, then shutting their door should be sufficient and the parents are being obnoxious, rude and meddling, otherwise they should just make the damn bed and save the conflicts for bigger fish.
I rarely make my bed, but I am a grownup who moved out more than 14 years ago, it is my prerogative as it is my home that I have made for myself and my family . I will say that the times I do get all obsessed with keeping my bed made it really does help with keeping the rest of things looking nice as well, just seeing the bed looking pretty and neat makes me want to make other things around it pretty and neat.
Now if the bed making nagging is just one example of an oppressive amount of nagging about ones environment then that is understandable to be annoyed by too. If the OP is living in a situation where there is no freedom to ever make a mess at all while enjoying life that could be very detrimental to anyone's mental state and I could understand where the complaint is coming from. And J types can indeed be very pushy with an attitude that they are correct until proven otherwise regardless of any evidence supporting their opinion. My husband can get like that and it can become exhausting, he certainly knows how to nag well, he doesn't see it as nagging though, he sees it as stating what he knows and what he expects based on what he already knows, sometimes he needs reminded that life is much better when it is fluid and fun rather than work work work. What is the point of making everything nice if there is no time to enjoy how nice it all is because one is constantly striving to make it nice.