Historically? I'm currently reading Stephen Kotkin's Stalin which describes the conflicts between tsarists, socialists, and a sometimes insurgent right (Union of Russian Peoples). What happened in that case was that a mismanagement of the wartime economy led to food riots and distributional problems in urban areas. On February 23rd 1917, 7,000 women marched on International Women's day demanding bread and an end to Russia's dismal participation in the war. Within seven days, the tsar was asked by his staff to step down from office and transfer power to a provisional government. In short, the provisional government sucked and didn't solve any of the problem it had promised to: namely an end to war and bread. There still existed a power vacuum following the fall of the tsar. On the right, people demanded Nicholas II's 13-year old only son Alexei to be tsarevich under a reagent, or for a totally new monarch to take power. They reviled the neutered parliament which had existed in Nicholas II's final years, the Duma, as not just an ineffective and illegitimate method of ruling Russia, but somehow insulting to the divinity of the tsar and the autocracy.

On the left the most radical elements were soldiers at the front or sailors in the Baltic and Black seas (see: the mutiny of Battleship Potemkin in 1905). They were firmly Bolshevik and jived well with the idea that Lenin et. al. could bring about an immediate peace. General Brusilov, in 1917, even as the army was thoroughly demoralized and villages at the front were inundated with wounded, launched a surprise offensive against the weak flank of Austria. The idea came from the Provisional Government thinking that a winning offensive could stir the Russian peoples, inspire legitimacy in the government, and push back Bolshevik threats at a coup. No luck: the offensive ended miserable after some units refused to advance. Then, the anti-Bolshevik Kerensky attempted two coups, the second one ending with his suicide, in order to replace what was seen as a totally ineffective Provisional Government.

A "genuinely mass movement on the right" didn't exactly exist in Russia in the summer of 1917 since the political landscape had been fractured, in the largest sense, into pro-tsar and pro-socialist. In 1917 the vocal rightist elements demanded that elections be canceled and "that government leadership pass to strongmen." How did the soviets/Bolsheviks consolidate power? They came in and promised that they could do what the people wanted: give them food and give them peace. Lenin was vehemently anti-war, calling the Great War an imperialist undertaking which only hurt the little people of the world, and the socialists took credit for a spontaneous peasant collectivization phenomenon happening in the Russian interior. The Bolsheviks were actually very few in number and took advantage of huge power vacuums, mystique, and soldiers' anti-war radicalism to set up a nominal government.

In summation: What about the Russian economy made people so radical? This can only be speculative, of course, but on the face value of what soldiers and workers were saying in the broadsheets leading up to the October Revolution of 1917 was that there was massive internal disorder which successive moderate regimes failed to control. It was possibly the radicalism of competing claims which made radicalism attractive: the knowledge that the status quo is simply not working and something totally different was necessary. For Russia at this moment the stakes were at once huge and small. Huge, because millions of Russians had been killed or injured on the front and people were starving in the cities; and small because there wasn't much to lose by opting for a government which promised something totally different. Furthermore, in a power vaccuum there are competing solutions which must distinguish from each other and end up as diametrical opposites and drive one another into further radicalism.

I haven't yet read The Wages of Destruction which is Adam Tooze's economic history of the Nazi economy but that's probably the best place to answer your question.

Source: Stephen Kotkin, Stalin, Vol. 1, 2014

Depending on your definition of extremistic, you can possible substantiate how certain times of economical crisis were contributing factors in the development or spread of extremistic ideologies. However, it's not feasible -and very reductionist- to pose this as a logical or even necessary result. There are plenty of examples of economical crises leading to more balanced or tolerant ideologies or methods. It's very complex and it's difficult to pose any grand conclusions without doing a disservice to the specificity of any casus. That being said, there is a certain common trope though. Times of crisis are often moments during which people experiment with or are open to alternatives. They feel like something has to change and that they have little to lose, assuming that it can't possibly get worse. While this often leads to revolutionary changes, it's mostly common for governmental policy and popular ideology to swing back and forth between known extremist or balanced behaviour.

Nonetheless, during harsh times, it's very common for people to look for scapegoats. The most obvious targets are often minorities or those who have few means to protect themselves. The Nazi ideology is an extreme example of this. They did not limit themselves to blaming the Jewish for "weakening" the Volksgemeinschaft, anyone who did not fit in was a possible target. Including those with physical or psychological limitations/differences.