The relative exceptionality of player characters is going to vary from edition to edition and table to table. In any case, it's not something that has any in-game meaning, so it has no effect on how someone reacts to that character. I don't know if there's ever been an edition where a level 1 fighter with short sword can easily dispatch 90% of opponents, unless you're counting old editions and level-zero NPCs, which will still vary from table to table. In the world of D&D 5E, a fighter who is more comfortable with a short sword than with a rapier is a superstitious fool, and will be treated as such by any professional who knows better (mercenaries, guards, etc).
In reality, I don't think it's going to come up much. There is no sane reason why a proficient character would prefer a single short sword over a rapier, and most players don't want to play that kind of character. Most players want to play characters who are at least marginally competent, rather than ones who are too stupid to use the obviously superior weapon and too stubborn to take well-meaning advice on the off chance that they do make the objectively incorrect choice.
Sorry, I meant opponent as in "potential opponents" as in people the PC meets. Reffering to the people that a PC is drawn or drafted from when recruiting people willing to go on an adventure. I can see how my wording was confusing.
I sincerely doubt that a foolhardy gang of murder-hobos l would turn YOU away just because you didn't have a machine gun and were using a "sub optimal pistol" or whatever. Also, I'll take a ride to work even if your car is sub-optimal, and I doubt either of us are as skilled as a fighter or driver or whatever, ya know?
Historically militias and vigilantes use whatever is around. Really, really major battles were fought and won with people wearing crappy armor and using crappy weapons. It turns out people aren't that picky about who can lay their lives on the line for them.
(Heck, the US Military has done it multiple times in recent history. I doubt other countries soldiers crack jokes)
Perhaps a well trained soldier or guard might be rude, but a villager might also be afriad of a half-orc! An elf might say something rude to a dwarf! A burly guard might also mock a puny bard or mage! It shouldn't dissuade a player from playing one, or worse somehow encourage a DM to take their fun away and have people refuse to work with them in game.
And honestly, it's kind of a moot point, because the 5e DMG openly encourages you to adjust things for flavor by simply swapping them. If I were somehow bothered by the credulity of a player using a sub optimal weapon I would just say "Hey friend, go ahead and take the stats for a rapier and we'll just call it a short-sword on your character sheet. Thanks for coming over."
The rules for HP and damage in D&D are so hysterically abstract and goofy it seems weird to get hung up on the realism of it as seen through the eyes of an NPC. How does that guard treat a monk who signs up for a quest? Does he know my stat block and class BEFORE he makes jokes about my weapon? Does he check to see if I am a multi-class or a sorcerer or something first or what? Wouldn't every guy and gal with nice armor be someone you at least ASSUME has the POTENTIAL to have a weird magic short sword that turns everything it hits into a toad before he says anything too snarky?
I don't really care what my players use, I'm not gonna shame them over math. That's like inviting someone over to your house and yelling at them for not liking asparagus. I just can't see the POINT in caring, but your group and mileage may vary.