Shaykh Muhammad bin Rabee' - a Salafi scholar from the city of Madeenah, former professor at the Islamic University of Madeenah - made a brief comment regarding the Woolwich killing - he stated (see this tweet):

Islaam is free of this barbaric act. No [sound] intellect accepts this type of behaviour. This will do nothing but incite people who live in these lands to have hostility towards the Muslims. This man is either someone who adheres to the way of the Khawaarij (an extreme sect of renegades) or someone who is intoxicated by his emotions and is totally ignorant of the rulings of Islam. Islam is a religion of justice and fairness. This is nothing but a criminal act.

The statement of the Shaykh, "intoxicated by his emotions" is a nice characterization of these types of people in general because they are intoxicated by the evil misguided opinions and sentiments of ignorant pseudo-scholars such as Omar Bakri, Abu Qatada, Abu Hamzah and their likes. Indeed the Messenger of Allaah (sallallaahu alayhi wasallam) said about the Kharijites that they are "youthful of age, foolish of mind" and from the greatest of their traits is rank ignorance of Islam and its rulings. These people (and in particular their leaders who misguide them) are a scourge upon the Muslim nation and the Messenger (sallallaahu alayhi wasallam) informed that they will continuously appear in the Muslim nation until the Antichrist appears in the midst (see here). For this reason it is obligatory upon the Muslims to wage war against them, their leaders and figureheads, refute and demolish their beliefs, their evil ideas, their vile methodologies and to exonerate Islam from their falsehood, since cutting these people off is a desired affair in the Shari'ah of Islam (see this article).