How bad of a thing do you have to do, in order to forfeit your right to live? Commit murder? Rape? Neglect or abuse a child? Abuse a wife or girlfriend? Exploit someone sexually? Engage in bullying? Sell addictive drugs that turn people into zombies?
If you just limit "they don't deserve to live" to the categories above, you will see that already many, many people do not deserve to live. Perhaps 50% of the population, perhaps more. Maybe close to 90%.
But just because someone doesn't deserve to live, doesn't mean that you or I have the right to be the one to take their life away. We are not the Judge of the World. As Gandalf said to Frodo, "Many live that deserve death. And many die that deserve life. Can you give it to them? Then do not be so quick to deal out death."
Some people deserve punishments that it would be absolutely, morally wrong for any other human being to give to them. For example, if someone has tortured others, he deserves himself to be tortured. But it is absolutely wrong to torture another person, no matter what he has done, so no human being can justly give such a person the punishment he deserves.
Another problem is the problem of uncertainty. In the Internet age, the entire country can get the idea that someone said or did something that they never said or did. Their reputation is ruined forever. Given that we don't always know exactly what happened, we should be even more cautious about making the call that someone deserves this or that.
Now, maybe what you're asking is whether the State ought to the take the lives of the people listed. I believe that when someone commits deliberate murder, the State has a right and a duty to take their life. "A life for a life" is just. But, in order to avoid accidentally executing an innocent person, we should have very high standards for when a deliberate murder has been proved. I get that our criminal-justice system is deeply broken, but that's probably a topic for another question.
While I have a lot of sympathy for vigilantes, I think they are in the wrong. As soon as people start taking vengeance in an unofficial capacity, it leads to feuds, wars, kangaroo courts and mob "justice." None of us want to be beaten to death by an angry mob that got the wrong idea. None of us want to be the victims of a witch hunt. We can help by not creating a climate of vigilante violence.