Muslims are offended when the Prophet Muhammad is disrespected, but don't respect others' religious sentiments. Why?

This is a right observation. When man grows emotional, he develops contradictory behavior. What Muslims are doing is not in conformance with Islam because they only know their emotions and nothing else. The so-called Muslim leaders have found a way to gain cheap popularity by inciting Muslims to react. Let me cite an event from history. Ibn Taimiyyah wrote a book on the topic of disrespect of Prophet Muhammad in reaction to an instance where a Christian had said something disrespectful about the Prophet. He mobilized a crowd of people through speeches and took them to the court of the Turkish Sultan. The Sultan was angry and had Ibn Taimiyaah flogged saying that people were not even aware and it were his fiery speeches that incited them and made them negative. He sent Ibn Taimiyyah back!

Same events are being repeated today. The controversial video was not even known before the so-called Muslim leaders raised such hue and cry. Blameworthy therefore is not the common man but the clerics and leaders who misguide them through emotionally provocative speeches.