This is completely and demonstrably wrong.
The Islamist movement is not a relatively recent phenomenon. It's a revivalist movement founded in response to three main events: failed rebellions against 19th Century British rule in India, Ottoman-Russian wars culminating in the War of 1877–78, and the demise of the Ottoman Caliphate in 1924. The Muslim Brotherhood was founded in 1928.
There is no workable distinction between politics and religion in Islamic orthodoxy. Hamas (which describes itself as "the Muslim Brotherhood in Palestine") literally quotes a verse from the highest Islamic authority (Quran and Hadiths) in their charter:
"The Day of Judgement will not come about until Muslims fight the Jews, when the Jew will hide behind stones and trees. The stones and trees will say O Muslims, O Abdullah, there is a Jew behind me, come and kill him."
There are probably a hundred other verses in the Quran and Hadiths instructing Muslims to fight and kill infidels.
More quotes from Hamas' charter:
"Allah is its goal, the Prophet is the model, the Qur'an its constitution, jihad its path, and death for the sake of Allah its most sublime belief."
"Nationalism, from the point of view of the Islamic Resistance Movement, is part of the religious creed"
"The day that enemies usurp part of Muslim land, Jihad becomes the individual duty of every Muslim"
"Palestinian problem is a religious problem"
This rhetoric from Hamas in the 80s is no different than the rhetoric from 1947. In 1947, the Muslim Brotherhood was fighting in Palestine, as was the "Jihad al-Muqadas" (Army of the Holy War).
“We must inculcate in the heart of every Arab,” he said, "hatred for the Jews" and we must the renew "the jihad against Israel" (“Emil Ghoury’s Response to the Telegraph on the Matter of the Refugees”, August 1948)
"The UN [partition] decision [of 29 November 1947] has united all Arabs, as they have never been united before, not even against the Crusaders ... [A Jewish state] has no chance to survive now that the ‘holy war’ has been declared. All the Jews will eventually be massacred" (Nadia Lourie, “interview with Mrs. Mogannam”, 10 January 1948, CZA S25-9005)
Within two days 2,000 men were registered, and it was said that 200,000 were "ready to perform jihad and sacrifice their lives".
"The Saudi religious authorities, the ulama, played a major part in the mobilisation for jihad."
"The call for jihad also vibrated throughout the Maghreb and thousands of Moroccan, Algerian and Tunisian Muslims in the spring and summer of 1948 set off to fight in the hills of Palestine (though only hundreds actually reached the battlefields due to French, British and Egyptian interdiction along the way)."
Madawi Al-Rasheed, “Saudi Arabia and the 1948 Palestine War: Beyond Official History,” in Eugene Rogan and Avi Shlaim, eds., The War for Palestine (2nd ed.), 240.