their religion actually does mandate capital punishment ... unlike any other modern religion.
Biased much?
The main religious text of every Abrahamic religion promotes violence and killing. The Old Testament is still cited by fundamental Christians (see the U.S.) and Jews (see Israel) to legitimize their violent acts. It may not necessarily be violence to other religions, but it's still violence. (I don't know the other religious texts nearly as well so I can't really speak for them, but I'm certain some non-Abrahamic religions promote some form of religious violence in their text as well.)
But the mainstream Jews and Christians have moved away from the extremes of their ideology and on to more moderate viewpoints. They're still picking and choosing the passages to interpret and follow, but now they're picking the less extreme passages and interpreting them in more moderate ways. The fundamentalists in Christianity and Judiasm are marginalized, and given little to no attention (with the exceptions being the fundamental population of Christians in the U.S. and Jews in Israel, and even then, they're kept in check by equally loud or louder moderate voices).
Muslim extremism is still very much in the limelight of their religion. The extreme viewpoints are constantly in the news, constantly being talked about. Hell, the most wealthy, powerful, and famous Muslims, who often act as role models for many other Muslims, are all extremists. Look at the leaders of Saudi Arabia or Iran, who are clearly extremists. Extremism is given significant attention. There are entire political parties dedicated to extreme interpretations of the Koran. And even if they're discouraged from the extremes, Muslims are exposed to it from youth. Hell, we're all exposed to Muslim extremism from youth.
That is the difference. That is where Islam is currently at, not at the opposite end of "modern religions" but merely a few centuries behind. Islam is currently where Christianity was a few hundred years ago, and is where Judiasm was a thousand years ago. The big question is how to get everybody to reach the points of moderation that Christianity and Judiasm are at. How do you marginalize the extremists?
Denouncing the religion as bad, as you are doing, will not serve those ends. Continuing to bring to attention the violent aspects of the Muslim faith is exactly what people don't do to Christianity and Judiasm (or any other religion for that matter). Implying that it should be gone, as you are doing, is no different than a Muslim person trying to get rid of you for being non-Muslim.
In fact, I'll go a little further and say that the perspective you've taken is exactly the perspective of Muslim extremists. The only difference between you and a terrorist is you haven't quite gotten there. You're still only talking about how bad it is, rather than doing anything about it. Why? I don't know. Maybe you're suppressing that ultimate conclusion to keep your morality. Maybe you're living too comfortable a life and don't want to lose your lifestyle. Maybe you're a coward and trying to incite other people to do what you can't. Maybe it's a combination of multiple factors.
That is, of course, the solution. You can't exactly make people cowards, but you can allow them better lives, and promote less extreme versions of their ideology. You can promote the moderate aspects instead of putting the entire religion of Islam on the defensive. You can denounce government leaders or religious leaders who hold extreme viewpoints, and maybe not prop them up as allies or business partners. You can help make the extremists poor and the moderates wealthy, the extremists weak and the moderates powerful, thereby setting role models who are moderate rather than extreme. These things will help, maybe not right away, but over the course of a generation or two, things will change.
What you're saying and trying to imply will not.