Your dog can see every person on the pavement through the mesh. They rush forward, bark, and watch that person walk away. A screen door can become a daily place to practice a reaction, even when the dog is friendly elsewhere.
First, check the door. A screen is not a reliable barrier if your dog can push through, tear it, or reach a passerby's hand. Keep your dog away from it when you cannot supervise. Use a closed solid door, a secure gate farther inside, or an opaque section that blocks the view. You can still let air in through a safe alternative if available, the dog doesn't need full street access to enjoy the room.
Teach a turn away from the door
Practice a cheerful "come inside" cue when no one is passing. Reward your dog for coming to a mat away from the threshold, then release. Later, with a person at a comfortable distance and the door safely secured, reward your dog for noticing and turning back to you before barking begins. End the short session before the street gets busy.
If a passerby appears unexpectedly and your dog cannot respond, close the view and move away instead of repeating the cue louder. If they have pushed against the screen, snapped through it, or redirected onto someone inside, ask a qualified, reward-based behavior professional for a safety plan. A screen is useful for airflow, it should not be your dog's job to patrol it all day. For a wider doorway plan, see the doorway and visitor guide, keep the screen door from becoming another place to rehearse rushing and barking
Sources: Best Friends Animal Society: Managing dog barrier aggression and frustration. American Kennel Club: Does Your Dog Bark Out the Window?.