I think we should distinguish the environment of Night City before we decide what is acceptable, unacceptable and what is frowned upon.
I have spent time reading forums and fan sites referencing Cyberpunk 2020 to better understand R.Talsorian's view of his creation.
I link this extract by way of reference;
Cyberpunk 2.0.2.0 is the second edition of the "Roleplaying game of the dark future" by R.Talsorian games. It is set in a the year 2020 of a dystopic alternate timeline starting 1990 where the world economy, social and political order has collapsed multiple times, and is in an ongoing disarray. Huge multinational corporations are the new powers that be, while most sovereign states have been forced to become supporting entities for the former. Technology, especially cybernetic augmentation and the Net has permeated the globe, but combined with the greatly deepened socio-economic chasm between the rich and the poor, such technologies have quite extraordinary, techno-primitive manifestations at the street level.
The characters in Cyberpunk 2.0.2.0 are the edgerunners. Independent souls that have rejected both the polished slavery of the giant corporations and the squalid misery of the street, they embrace their changing world and take control of their destinies. They have chips in their brains, interface plugs in their wrists, binary code in their soul. They are the cyberpunks.
My understanding is that Talsorian very much wanted a realistic environment, close to the attitudes people had in the 1980's. I have also used popular films for reference (Bladrunner, Robocop, etc).
In a world where security and safety is reserved for the rich and powerful. People have become accustomed to carrying personal side arms for their own protection, but this is only seen in the slums and poorer districts.
In the larger cities it is still socially unacceptable (and illegal) to carry weapons. This does not seem to stop the private security forces that can afford to pay the police to look in the other direction.
However, in the boostergang districts (And any other gangs), where police presence is non-existent, social niceties are thrown out the window. The gangs become the law, and have their own rules. However, if your not in the gang, you will defiantly not be aloud any visible weapon, or you will be deemed a threat, and most likely shot.
I think my conclusion is summed up like this. If your in the large cities and not a cop, private security force or very rich, then the cops will stop you if your carrying an overt weapon, they might be bribed to look the other way, confiscate the weapon, or just arrest you.
If your in the slums or poor districts, then you can get away with 'personal protection' weapons, the police, if there is any, will probably turn a blind eye. That being said, strolling around with an AK47, will raise some eyebrows, any may attract unwanted attention.
If your in the gang territories, and not part of the gang, watch out. Your more likely to be shot on sight for being a threat than anything else.
To that end, covert weapons, small weapons placed under coats (even SMG's can be covert in a shoulder sling under a jacket) would be your everyday setup, and you would only 'tool up' on a specific operations.