It turns out this happened before with the net neutrality banner. The banner has received some updates so the script is different this time. In time, I'll write something that uses cross-domain storage to remember if you have dismissed the banner once (as opposed to dismissing it always, even before you see it the first time):

// ==UserScript==
// @name        Stack Exchange Dismiss Announcement Banner
// @namespace   https://github.com/Glorfindel83/
// @description Automatically dismisses an announcement banner whenever you visit a (new) site.
// @author      Glorfindel
// @version     0.1
// @match       *://*.stackexchange.com/*
// @match       *://*.stackoverflow.com/*
// @match       *://*.superuser.com/*
// @match       *://*.serverfault.com/*
// @match       *://*.askubuntu.com/*
// @match       *://*.stackapps.com/*
// @match       *://*.mathoverflow.net/*
// @grant       none
// ==/UserScript==

(function () {
  "use strict";
  setTimeout(function() {
    $("div#announcement-banner a.js-dismiss").click();
  }, 100);
})();

It turns out this happened before with the Net Neutrality banner. It now happens again with the podcast with the new CEO, so I've modified the script and officially launched it on Stack Apps:

Dismiss Announcement Banner

(GitHub link for direct installation)

It uses cross-domain storage to remember if you have dismissed the banner, so every time you see one it's guaranteed to be one you've never seen before.