Click bait!
Well I just saw the movie, and now the thread is closed, and I have so much to say! Actually not really: I enjoyed it, it was amusing, the acting was decent, the plot was alright, effects were good, and the inclusion of Maul was cool. It sits comfortably alongside Rogue One in terms of re-watchability I think...which unfortunately isn't saying that much, but I do think it's a welcome addition to the canon.
But was it murder? Yes, legally it was murder. The reason people had to have their guns in their holster before a shoot out was so that witnesses could describe who drew first. The person who drew first was the murderer, and the person who drew second was acting in self-defence. That's why there's so much drama in the moment: each participant is trying to get the other to go first. If those weren't the rules, then who would ever wait? Somehow this simple legal fact has been lost, and audiences these days have no clue.
(The irony is that, using today's technology with slow-motion and measuring reaction times, we can actually prove that reacting is faster than acting. Reacting uses shorter circuits in the nervous system, which kind of makes sense when you think about evolutionary development. The person who draws second can actually often get their shot off before the first mover has fired.)
In E4, when Han did shoot first, Greedo already had his blaster drawn, so Han shooting first doesn't make him the murderer...the gun is already in his face. For some reason, Lucas got bamboozled by people who didn't know the simple duel rules, so he edited it differently later, sadly. But the edit makes no sense: was Han supposed to wait for Greedo to actually pull the trigger? That's not a large window of opportunity for self-defence.
In Solo, Han is Greedo, he already has his blaster out. But he also shot first, before giving his opponent a chance to draw. Ergo: murder. It really is that simple.
So it was murder, but was it also the right thing to do? Maybe. That's a tougher question IMHO. Beckett was a dangerous person and very handy with his own gun, not somebody you want to duel with, or want after you. It seemed like they had a relationship where Han could have stunned him and left a vial of "Unobtanium" in his pocket when he woke up to smooth things over...but maybe not. I'd have preferred that, personally, because the shooting takes away from the later assertion that Han is a "good guy". Right now he's more like Cassian Andor from Rogue One.
Anyway, hopefully those who respond to this click-bait will keep it civil, or simply agree to disagree.