I could be wrong, but I think they're saying they do not, but many prisons have a rule against that anyway.

I'd argue it's something to do with decency, appearance, atmosphere, given that (at least in my culture) while T-shirts are fine, sleeveless shirts are seen as rather trashy.

I agree with you. I do find your choice of word "decency" troubling to me. Dress codes are often about control and shame of the poor and in a prison visitors lobby that seems about right. This seems less about decency and more about telling poor people their clothes are not nice enough for a prison which is kind of funny considering prisons are purpose built to be among the worst places in existence in our society.

Trashy is sort of a slur on the poor. Not trying to call you out or anything, maybe there's a better word that trashy aka saying a person is like trash.

Lots of prisons have dress codes for visitors of prisoners banning visitors from certain kinds of clothing. On the banned list of items, you will never see Burberry tweed or men's sport coats, but rather t-shirts, types of shorts or other clothes poor people wear (often called "trashy" clothing). It's about shame and control.

The link below shows a cross section of expensive designer fashion, exclusively for rich people. Almost all of it would be banned by prison dress codes.

https://duckduckgo.com/?q=expensive+designer+fashion+runway&...

Now I'm just picturing catwalk models marching into a prison dressed like that. Like a scene from Zoolander. :-)

Perhaps a reference to Prison Break, where a character had a map of the prison tattood to his body? Just a guess.

They are talking about visitors to prisoners. See my post above, but these dress codes are what dress codes are always for - control and/or shame.