The clearest way of explaining the seriousness of this vice is through current events. While all terrorism is evil, terrorist acts committed in the name of God are particularly evil. This is why Islamic terrorism is so vile; they claim that God condones their behavior. On a related note, the leader of the Neturei Karta, Moshe Hirsch, recently passed away. A telling analysis of this anti-Semitic Jew's life comes from none other than an anti-Semitic Palestinian official: "We consider Rabbi Hirsch a part of the Palestinian people." Hirsch's life was a constant Chilul Hashem. Both he and his followers went well beyond legitimate philosophical disagreements and into the realm of endorsing evil in the name of God.
Although I have no respect for how Hirsch lived his life, it's important not to be overly indecent when condemning him. The reason I bring this up is because there was an obituary written about him (the theme of which is quite Orwellian), but the comments following the piece were also troubling. We must always remember that the way in which we talk about others often reflects more on us than on the people we are talking about. We can - and should - speak out against those who harm the Jewish people, but we must do so in as respectful a manner as possible. Because when we don't, it doesn't reflect well upon those of us who truly stand for God-based goodness. And worst of all, it can turn into a Chilul Hashem - the exact infraction we're trying to avoid.
When people see kind, considerate, and honest Jews, it brings great credit to our Jewishness. In addition, when we create a Kiddush Hashem, God Himself says, "You are My servant, O Israel, in whom I take pride" (Isaiah 49:3). I witnessed this first-hand for many years while working as a waiter at a kosher restaurant. Whenever there was a recognizably Jewish family who was well-behaved, it created a tremendous Kiddush Hashem to everyone else present - whether Jew or non-Jew. However, whenever recognizably Jewish families were poorly-behaved and interfering with other people trying to enjoy their meals, it created a terrible Chilul Hashem.
This whole topic can be summed up concisely: for better or for worse, our behavior defines us.