Was it necessary for the plot for Romero and Gideon to die?

Necessary is subjective in that, was there another way to convey a message? Yeah sure, you could get messages across without the killings, but would it work the same? Gideon was murdered by a nobody. Just an everyday guy who got hurt in the fsociety hack apparently. He wrongly believes Gideon (another innocent) of being the cause. He takes out his frustrations. The symbolism at this time in the show is that the hack was going to have real world implications for the common person...not just hackers and big corporations. The little nameless guy is in this mess too and he can be provoked to violence. This is also reinforced by the woman trying to pay her mortgage at the bank or something. The hack has messed up much more than perhaps the fsociety hackers expected.

Another symbol was when they released all the dogs at the vet's office. When they return again to burn the lawyers body, they are informed that all the dogs are back anyway. Freedom was just temporary for the dogs just like, perhaps, everyone else.

Romero? Well his death, all the way up to the last episode, was a misdirection. Was it Dark Army? Was it Elliot/Mr. Robot? Was it Tyrell? Nope...an accident from a neighbor's gun. But for awhile it made people very afraid. Completely meaningless death. Yet, the irony is that investigation into his death gave us the FBI illegal surveillance plan. It gave Dom the tip that led to Mobley and fsociety HQ and a number of other arcs.

Can all this be written without killing them. Yeah sure...I guess, but I think this way worked pretty well. Gideon was a jaw-dropper and classic, "Didn't see that coming". Romero had everyone puzzling away for the shooter ID.

Both deaths were very sad. I think the circumstances surrounding Gideon's death that made his death so powerful was he such a good man, complete innocent and killed by association.

Romero's death was important to plot because it made everyone in fsociety paranoid that they were being picked off by the DA, they were sure Romero's death was DA related and at anytime anyone of them could be next. As a result it made the FBI easier to track them - as Dom said they all scattered, aka Python. When in reality Romero was killed by a random bullet shot by a neighbor - a complete accident.

Both death's were sad and they were two of my favorite characters, however I think they were necessary for the storytelling.

I agree.

Seeing as how Romero has a new role on Luke Cage, maybe he requested/needed to be killed off to further his career. Happens a lot actually.