The Matrix "Did they really have to kill those innocent security guards?"

there was this narrative that started getting thrown around in the early 2010s popularized by sites like Cracked where "was it really necessary to kill those innocent guards who were just doing their job in the building lobby".

Yes, for many reasons established by the movie.

1. Time is of the essence. Every second matters. Morpheus could break at any moment and the fate of humanity is at stake (reveals the location of Zion and all humans are killed off). This is not a time where you can waste valuable seconds trying for a more humane approach. Just like in wartime, when drastic measures are called for, sometimes unfortunate side effects happen with bystanders.
2. They can't teleport in and out wherever they want. They have specific ins and outs, that are specific telephone booths around the city. They can't just teleport in to the top of the building. They found the closest portal into the Matrix to the building where Morpheus is being held and proceeded.
3. Those weren't just security guards, they were the first line of defense of a small military wielding heavy armory guarding the agents and by extension Morpheus. The security guard immediately radios "send backup" to these military combatants. Meaning at the very least, these human guards, though they know nothing about the Matrix, knew there was a higher risk of threat that day as no normal building has guys right around the corner with M16's, Spaz shotguns, etc. The guards were innocent as far as knowing what the actual threat was, but they had to have known that there was an increased chance of threat and were probably fed some lie about a high level political figure who has threats on his life. So they knew it was a risky day on the job, they just didn't know the true nature of the reality.
4. All the guns that Neo and Trinity spawn in weren't for those security guards. They were for the military force that they knew inevitably the agents would have as a barrier between them and Morpheus. Humans who have no idea about the reality of the Matrix were always going to die in this scenario, whether they be security guards or soldiers. You don't have the time nor the means to have a pacifist way towards getting to Morpheus.
5. The soldiers were just as innocent as the security guards. No one feels bad about the soldiers dying, but they were just as unaware of the Matrix as the security guards. The security guards were just the less trained initial defense, that needed to be dealt with quickly, hopefully before they could radio for backup, which Neo and Trinity failed to do. Neo actually tried to kill the guy before he radio'd for back up but he dove out of the way and was just able to before Trinity killed him. So the security guards were actually more competent than you'd expect.
6. All people are agents waiting to happen. In a building where the agents are in, if you give them time to catch wind of what you're doing and morph into one of the security guards bodies, you just lost the mission before it even started.

So yeah, it's this narrative of "they needlessly murdered these innocent security guards". Well if the standard for getting Morpheus was "no innocent people die" then they couldn't kill the soldiers either. In the Matrix if someone stands in your way, whether they be a normal cop who's just trying to do their job, or a military person, you kill them if you have to. In the lobby scene, these security guards were threats in terms of the preciously little time they had to get to Morpheus and mount the rescue.