Saying "Starfleet isn't a military" doesn't excuse their lack of common sense. If they feel it's necessary to arm their personnel, they should feel it necessary to give their personnel some sort of body armour. Especially on DS9 where we do see dedicated infantry personnel in Nor the Battle to the Strong or The Siege of AR-558.Staying on the subject of the military side, the MACO's were equipped for military operations but when in for instance in DS9, Starfleet personnel were involved in military operations as well as going into warzones but didn't have any body armour. Starfleet didn't want to be associated as a military organisation but considering armour has been part of martial philosophy since the dawn of time, it didn't make sense that Starfleet personal not to have them?
This is something which Disco has corrected, at least.