When he was retreating towards the police with a mob in hot pursuit, he had only shot one person, and wasn't shooting at anyone else until he was attacked. There was no reason for anyone at that point to believe he was an active shooter, as he wasn't actively shooting.
The area in question is pretty small, and the protestors, from what I've seen, all seemed to be communicating, as well as can be expected. After the first shots were fired, and Rittenhouse was seen on the move and still armed, I'd assume he was an active shooter if I saw him.
That's your theory, I suppose. Mine is that the were attempting to stop some who they knew had shot one person, as that's what the crowd was saying. They could have just been trying to take revenge on him. At least one guy learned a lesson about attacking someone with a rifle: if you've got a pistol, don't advance to point black range to use it.
Honestly, I don't have a theory yet.
Just acknowledging all of the possibilities.
In the end the truth probably lies somewhere in between. My full, and honest take on the situation-
Shooting engagement #1: The first victim (Rosenbaum ) was being belligerent, and overtly aggressive towards the now isolated Rittenhouse. Nervous, and unprepared for such a set of circumstances, Rittenhouse allowed himself to get cornered near the parked cars at the scene of the first shooting. There's no known video [at least at this time] of the interaction between Rosenbaum and Rittenhouse prior to the short foot chase towards the parked cars, so it's impossible to know the unarmed Rosenbaum's intentions in pursuing the armed Rittenhouse.
Shooting engagement #2: Following the initial shooting, and clearly seeing that Rittenhouse was not only the perpetrator, but also still armed, the three primary subjects of the next engagement pursued Rittenhouse (perceiving him as a threat to other protestors). From what I've seen, Rittenhouse clearly left himself very vulnerable to the crowd providing at least three people the opening to approach him directly.
In the end Rittenhouse was clearly not mature/ experienced enough to handle the responsibility of the firearm, and ended up putting himself into a situation where he was compelled to use it against Rosenbaum. Rittenhouse probably felt brave enough (and to an extent useless, next to the other clearly more experienced armed 'militia' types actually guarding the business) to wander off by himself. That is based off of his earlier statement that he'd 'go into harm's way.' And I'm going to go out on a limb and say that Rosembaum took advantage of the situation.
If I'm being generous, I'd lay the responsibility for the first shooting 50% - 50% on both parties (Rosenbaum and Rittenhouse). But, Rittenhouse ultimately made the decisions that created the scenario (wandering off on his own, getting cornered between parked cars, bringing the Rifle to the situation in the first place).
For the second shooting, all I can say is that if confronted with the same situation, I can only hope that I'd have the same courage as the three men we've seen engage and attempt to disarm Rittenhouse. Maybe some better tactics, based of previous training, but still with the same level of courage to approach an imminent and well armed threat.
In the end though, even once Rittenhouse wandered off on his own, the two subsequent murders could've likely been avoided if he had properly used the rifle in the first place. If he had, once initially approached brought the rifle up to a shooting position and kept Rosenbaum in his sights, Rosenbaum likely would've backed down.
Similarly, when he was being pursued, if he had stood his ground, rather than turned his back to the people approaching him, he could've used the threat of the rifle to pause the situation until the police arrived. Also, and this is important, he failed to use his "medic kit" on Rosenbaum after his ability to threaten Rittenhouse was clearly neutralized. If Rittenhouse, after shooting Rosenbaum, had instantly shouldered his rifle and started first aid, the whole situation would've been different and he likely could've justified the self defense claim.
Bit lengthly, I know, but it's a complex situation.