Not speaking for the Catholic Church - I don’t support the death penalty and I’m Catholic. Pro life means Pro life all the time. As long as there’s life, there’s hope. I don’t support state/government endorsed murder, be it abortion or the death penalty. I have no problem with a parent killing the person who raped their kid or pther such instances.
It reminds me of the Terri Schiavo thing. I didn’t support the government getting involved in that, or the polictians on both sides who used this woman for their personal and political benefit- none of that helped Terri, not the parents or the husband or the media or the politiians. It should have never been something the public knew about. If the public was interested in the decisions I made when my parents were dying, I’m sure many would think of me as a murderer and many others would think of me as something of an angel. It was nobody’s business and because the public didn’t know, they couldn’t comment on it and because we kept it in the family, it was about the family. And some didn’t understand, how I could stop all outside/medical help so he and she could die in peace. One of my brothers even said at her funeral when asked what my mother died of, that she died of a morphine overdose, because according to him I gave her too much morphine. I would never want what I did or how I handled my parents last days to be public knowledge or considered public opinion or that the public had any say in what I did for my parents. I don’t know how the Terri Shiavo thing happened or why so many were interested. I’m happy that whatever goes on in my family isn’t open to discussion to complete strangers or the government.
Your question regarding Catholics who advocate the death penalty can’t be really Catholic is something I don’t know. I do know anyone who supports abortion/choice isn’t following the teachings of the catholic church. Personally, I think that applies to the death penalty. But I’m also all about hanging or killing those who are treasonous, I wouldn’t have a problem with that at all so I’m not a very good Catholic in that sense. I also don’t have a problem with a parent dealing with a pervert who violated their kid. I just don’t agree with the State or the government having that kind of power.
When B16 was pre-16, he explained that one could be in favor of the death penalty, among other things, and still be in good standing. Abortion and euthanasia are not on that list. So, your personal opinion on this matter doesn't match that of the Church.