No, like people dont walk around literal warzones wearing amour and bearing arms all the time. Including soldiers.
Historically in Europe after the fall of Rome till around the 18th century many if not most people were armed.
The minimum would be an eating knife but daggers , hangers (what D&D calls a short sword) and other swords were carried along with bucklers by large numbers of people. Clubs or all kinds were common and there is at least one case of someone going out to a bite at a tavern and having to kill someone with his longbow.
This went on with the addition of pistols, blackjacks and other small and concealed weapons well into the Victorian era.
What would have been unusual is visible armor or weapons of war. This means polearms, great swords which were essentially used as polearms, maces , warhammers and the like were not usually carried,. That longbow was probably a caseof the guy stopping for a drink after target practice and things going terribly wrong.
For non Americans.
A good analogy would be the contemporary USA where in many states pistols are fine for civilians to carry either open or concealed depending on local law and custom hunting arms are fine out in the country.
In most places an AR15 would be provocative or impolite in many cases outside of security situation or shooting practice even though such weapons are nigh ubiquitous. Its sufficiently ingrained that even pro gun carry people consider it very bad form.
Wearing armor too is not common, I have seen soft body armor a time or two worn by civilians and armor like jackets . Its not thought necessary but if people can't see it they don't care.No one outside of a security situation or practice wears anything like the armor you wore. If you can see it, not OK.
D&D worlds are more dangerous though and while common sense and comfort might limit what is carried, I'd guess everyone other than very young children, criminals or slaves is probably armed