I worked for the DoD on a project in Iraq and saw some interactions between Special Forces groups. Spent a lot of time with Rangers from Hunter AAF in Georgia. I think this scene employs a bit of artistic license to help set up story points later in the film.
To the heart of your question, I'd think a Delta Sergeant would pull him aside and have him flip the safety in private. They are arrogant, not stupid.
Captain Steele approaches Hoot and says:
Delta or no Delta, that's a hot weapon. You know better than that. Your safety should be on at all times on base.
And Hoot replies while wriggling his finger:
Well, this is my safety, sir.
Then turns and walks away.
Steele then says to Delta Sergeant Sanderson a couple of lines later:
You Delta boys are a bunch of undisciplined cowboys.
Can't see any other implied conclusion than Delta can do just about as they please. I'd think it's a bit of an exaggeration to play up the rivalry and tension between the Rangers and Delta operators. It acts as foreshadowing to set up some of the problems with miscommunication and lack of cooperation that occurred initially in the firefight in town that led to mission breakdown. Conversely, it also heightens the sacrifice Delta snipers Shughart and Gordon made giving up their lives to protect Nightstalker pilot Michael Durant. Delta might have serious chips on their shoulders, but they are all brothers when it matters.
Mark Bowden, the author of "Black Hawk Down," wrote this in the Philadelphia Inquirer:
Steele watched with mounting distress as his formation broke down. He despised some of the Delta operators for their arrogance and their cocksure bravado. He respected their expertise and courage, but not their professionalism. They were disdainful of authority and discipline, and cavalier toward orders issued by anyone outside their tight, secret fraternity.
Now, an hour into the mission, the Rangers and Delta men were operating as separate units under competing commands. They even had different radio connections. Each Delta commando had a radio earpiece under his little plastic hockey-style helmet - Steele called them ``skateboard helmets'' - and a microphone that wrapped around to his mouth. The Delta men were in constant touch with one another, but not with the Rangers. The Rangers relied mostly on shouted orders. They hadn't perfected the elaborate hand signals the D-boys used when the noise of battle drowned out their radio talk.
Poor communications had come into play just minutes into the assault, when one side ended up literally shooting at the other. Howe and his Delta team had been on the roof of the target house, rounding up Somalian prisoners, when they fired at a Somali on a nearby rooftop. They were instantly peppered with return fire - not just from the Somali, but from a Ranger blocking position on the ground. A Ranger had evidently seen shooting from the roof and had fired away without checking it out.
Link to Inquirer story »
Here's the clip in question: