There are two schools of thought on this and both have pros and cons.
Carry with the safety on helps keep the owner and others safe from negligent discharges while out and about.These can happen in many ways. Trigger pressure that can set off the trigger can be asserted on the trigger by objects or circumstances without the knowledge of the wearer. This happens frequently enough to need to considered .
Then there is the gun grab reason. Since many attacks are close and physical in nature, the attacker can or will make an attempt to get control of the gun and turn it on it's owner.
If the safety is on the attacker will need precious seconds to figure which lever or which way up or down to throw the safety to on safe. This will give a the gun owner time for plan B. Could be for getting the gun back, running away, or drawing a backup weapon of some sort. Defense has to be in layers and a Plan B is vital.
For instance, at some the forums it is little discussed at times about plan B and it's needs or equipment used for such things. A lot of people have no plan B and think that just having the gun is enough.
Little trigger pressure is needed to set off a DAO or newer unconventional DA/SA guns like the Taurus, Glock, and HK families. This means more chance of a negligent discharge over conventional DA/SA pistol designs. Thus having the safety on makes sense.
Now for the other side of the coin. Carrying off safety.Here there is evidence for some to do such.
As has been written at this forum more than once, there are a few documented cases where is the heat of battle safeties were not wiped off to fire and the trigger pulled repeatedly with useless result. The result at the end of the confrontation was a dead or seriously wounded defender. Having the safety off to start with would have negated the incidents and the attacker would have been the casualty instead.
Practicing wiping the safety off and back on before reholstering is supposed to be practiced until it is second nature. People either bypass this for many reasons or over time get out of practice and mindset. We all need to practice different shooting areas. Time or other things may cause this to be ignored or put off.
So while it is a very good idea to have the safety on, it can be seen why others might not see it that way.
Personally, if it is a normal DA/SA pressured trigger of more substantial and more force is needed ( 10 to 14 pounds), then safety off makes some sense. Many semi-autos come with decockers only with this type of pistol. Then it makes sense for safety off. They don't have safties to wipe off. Or the heavier pull ones can be carried off safe by the user since the heavier pull gives a safety margin that have decockers and safties.
Some of this is stating the obvious, but needs to be written.
Do what you will. We are liable for our actions to ourselves and others. Morally too.
Under 10 pounds of pressure, safety on seems to be the better and safer choice.