It's not suicide bombing the problem. That's just the delivery method. The problem is suicide bombings targeting civilians. Now, it would be interesting to have the answer to the percentage of people in the western world thinking that "attacks on civilians can be justified to defend democracy". If the previous question was "Do you think the attacks on Hiroshima and Nagasaki were justified?", you probably won't like the numbers you get for the second question.
I think even if you ask "should the US use nuclear weapons in Syria, Iraq and Afghanistan," a large number of americans would say yes.
If you click the link, the parent has an entirely different analysis than the researchers, Pew. They say:
Muslim Publics Share Concerns about Extremist Groups
Much Diminished Support for Suicide Bombing
20% of Americans believe in a lot of things, from UFOs to a lot of nasty things. I invite you to do a quick search.
http://www.pewglobal.org/2013/09/10/muslim-publics-share-con...
Having 20% of the populace believe that suicide bombings are justifiable is a real problem.