changeDefaultToFollowingTab.user.js

// ==UserScript==
// @name         Change Default To "Following" Tab, Not "For You" Tab
// @namespace    http://tampermonkey.net/
// @version      0.1
// @description  try to take over the world!
// @author       You
// @match        https://twitter.com/*
// @icon         https://www.google.com/s2/favicons?sz=64&domain=twitter.com
// @grant        none
// ==/UserScript==

(function() {
    'use strict';
    const waitingTime = 200;
    let clicked = false;
    const findFollowingTab = () => {
        if (clicked) {
            return;
        }
        const tabs = document.querySelectorAll('[role="presentation"] a[href="/home"]');
        if (tabs.length > 0) {
            tabs[1].click();
            clicked = true;
        } else {
         setTimeout(findFollowingTab, waitingTime);
        }
    }
    window.onload = () => {
      console.log('Fired');
      setTimeout(findFollowingTab, waitingTime);
    };
})();

History

2023/01/23 fixed the bug of not switching the tab when the landing page is not Home.
2023/01/23 @match is more sophisticated. @include was deprecated.