Well for me an example of a functionalist analysis would be 9/11 conspiracy theories. The function they perform is to protect Islam. They allow anti establishment radicals to work to support the establishment. Functionalism is about understanding the stability of the system. So 9/11 conspiracy theories superficially seem threatening, destabilising and disruptive, while in reality, they are the opposite. Note lefties often like to accuse me of being a conspiracy theorist, when they're not accusing me of being a retard and know-nothing, or drawing attention to me, by telling every one that they're ignoring me.
But in fact I'm the opposite of a conspiracy theorist. I don't doubt that the vast majority of 9/11 truthers are totally genuine, I don't think they're all in some giant secret conspiracy to back up the establishment. Any more than I think that there's some giant secret Jewish supremacist conspiratorial network that instructs their members what to do, think and say. No absolutely not.
Jewish supremacism is so effective precisely because its not a conspiracy. Many Jewish supremacists are genuinely horrified by Benjamin Netanyahu and I don't doubt that Netanyahu's contempt for his fellow Jewish supremacists is also entirely genuine. Many Jewish supremacists are deeply, deeply uncomfortable with the actions of Priti Patel, the more so that she was clearly acting on the orders of the British Hilary Clinton (aka Theresa May).
So functionalism is understanding how extreme Judophillia and extreme Islamophillia support and stabilise the system, the establishment and the status Quo when superficially they may seem, threatening, destabilising and disruptive. How BDSM (Boycott, Divest, Sanctions Movement) supports the maintenance of our Saudi - Israel foreign policy.