I venture to suggest the answer is nothing, or perhaps nothing good. Because extremism, of any flavour, is not a creative impulse. It is wholly destructive. How do you recognise an extremist? By the constant outpouring of venom and hatred, aimed sometimes at opposite extremists, but more often than not, at normal folk going about their business.
In this display of hatred and intolerance, extremism differentiates itself from normal passion or single-mindedness. It is perfectly normal for someone, especially when young, to be wholly devoted to music or football to the virtual exclusion of everything else. That is passion, and without it there would be no greatness in the Arts or Sciences. But passion does not seek to impose its will on everyone else. Passion does not rush to judgment of others. The worst you can say of passion is that it may be oblivious to its surroundings, being wholly focused on its object.
Politics is supposed to be the art of the possible. That means it should be pragmatic. The pragmatic politician looks at a situation with a view to minimising the badness in it. Who is hurting? What can we do to help? Pragmatism is the politics of questions. This is where we are, what is broken, what should we do about it? Pragmatic politics is thinking politics, grown-up politics, problem solving. Unfortunately, it is also difficult politics, because it requires intelligence and hard work.
Then there is dogmatic politics, where the answers come before the questions. Where the answer to every situation is more (or less) taxation, less (or more) legislation, and so on. I'm not saying that reason is never exercised, but that it is always based on a few fundamental axioms that are never challenged (and may very well be wrong). Dogmatic politics breeds extremism simply because it is based on faith, not on reason.
However, simply holding highly partisan views does not constitute extremism. Paradoxically, the true extremist is one who sees extremists everywhere except in the mirror.
The political extremist thinks that most people in society have been brainwashed by the other side's propaganda. But, as extremists from opposite sides both think that, logically it must be nonsense (and it is). The vast majority of people hold some leftist, some rightist and some centrist views on different issues that don't have to conform to any ideology. And they want their politicians to be pragmatists. Or at least, they want their problems solved.
Religion has this in common with dogmatic politics - that it is based on faith. And, as with politics, it is everyone's right to entertain a belief system, whether it be a widely shared, traditional one or a wholly personal one. To hold none is also perfectly fine. What is not perfectly fine is aggressive proselytising. I know where to find several churches, mosques, synagogues and temples. I even know how to use bookshops, libraries and the Internet. So when I want to investigate a religion, there's nothing stopping me. It is also perfectly reasonable for religious folk to produce articles, books, movies even, promoting their faith. No-one who doesn't want to is obliged to seek them out.
Where it all goes pear-shaped is where people insist that their religion, and highly questionable 'facts' derived from it, should be taught to school children as truth. That insistence constitutes religious extremism. As does 'rudeness for God' where the over-zealous take their right of free speech to mean a right to threaten, insult and abuse all who don't share their views.
Again, it is natural that someone's religion will influence their voting pattern, whether as a private citizen or as an elected official. What is wholly unacceptable and certainly constitutes extremism is the insistence that a political party should follow a religious agenda (unless, of course, it is the democratically expressed wish of the majority of party members).
By Societal Extremists, I mean people who try to force society at large to conform to their particular agenda. Often these people are politically naive, with a grossly inflated view of the importance (to others) of their pet hate (and it's usually a hate). I may strongly desire an end to whaling, but it is your absolute right either not to care or simply not to want to talk about it right now. The extremist is one who cannot accept that others may not want to play their game.
Possibly the most notorious example of this is the abortion issue. Some insist that everyone has to label themselves pro-life or pro-choice. But it is simply unnecessary to play along, in a game that quickly degenerates into the hurling of foul slander, such as, you want to murder babies, if you dare to give a considered response. This substitution of banality for rationality is societal extremism of the worst sort and represents a true degradation of the human as a thinking species.
But enough from me. I'll leave you with my quotable quote of which I'm quite proud:
The true extremist sees extremists everywhere except in the mirror.
Thanks for reading!