The paper attempts to identify some of the characteristics of the system of the Western and Islamic values, ideas and attitudes in their radical forms and to give its comparative analysis. It has been shown that it is possible to talk not only about the Islamic, Christian, Protestant, Orthodox, but also about the liberal, democratic, conservative, communist fundamentalism, fundamentalism of human rights, market fundamentalism, etc. The main attention is paid to the ideas of the extreme right group of publicists, cartoonists, grouped around the magazine Charlie Hebdo in Paris and of one of the currents of the Salafi movements in Islam. It is shown that despite all the socio-cultural, political-cultural, ideological, political differences, these two phenomena are very close to each other in their objectives pursued, in the direction and results of operations, in the level of extremism. The author resumes that both phenomena are based on the systemic crisis of the modern world, where one of the key factors is the rejection of all taboos.