I do not understand how anybody can not support Rick with this.
Imagine that this shit was all real. That there was a zombie apocalypse, that you'd seen people die and lost people you loved. You knew that the majority of people are incredibly hostile and will kill you or seek to control you.
You manage to find a safe place. Somewhere with people who are great, but don't know what they're doing. Somewhere that has been slowly losing people for a long time because they don't understand how anything works. At all. Because they just ignore all of their problems and hope they go away.
So, something needs to be done. If you want to save as many people as you can, you have to make sure that people are punished when they do wrong. You have to make sure that everybody understands how shit works now so that they can protect themselves and their families.
None of this is deniable. At all. It takes very little logic to see this.
So, obviously, action needs to be taken and people who do wrong need to be punished. There has to be a consequence for doing something wrong, else you'll just keep doing it. That's why we have a judicial system.
But they can't imprison them. They do not have the resources and, should the prisoner escape, it takes very little for them to go on a mass revenge killing spree.
You can't exile them. If they survive, they could tell anybody about the town and you'd have a war on your hands almost instantly. They'd definitely hold a grudge and would make sure that you had to either die or lose as many people as possible to defend yourselves.
You kill them. It's the only possible way to ensure that the majority are safe.
Now, obviously, not everything warrants execution, even in the world of The Walking Dead. Some things are small enough that cutting somebodies rations or anything along those lines is acceptable and enough of a punishment to deter people from doing it. But when it comes down to it, if somebody in endangering the lives of others (you can see very clearly that the guy was a threat in general, not just to his wife. Violent temper, heavy drinker, already beating his wife. The second Rick disrespects him, he flips and starts attacking him) in this scenario and there's no hope of talking them down (which is incredibly obvious in this situation), you'd be an absolute moron not to kill them. It's horrible, it's unfair and it's not the ideal situation, but, in a zombie apocalypse, who the fuck gets an ideal situation?
If you honestly believe that Rick is in the wrong here, you're a fool.