Makes the Moodle schedule bearable.

MoodleSchedulePlusPlus.js

// ==UserScript==
// @name         MoodleSchedule++
// @namespace    https://gist.github.com/chhoumann/4f8a6c56838b04789060042d11e651de
// @version      0.1
// @description  Automatically goes to semester page and removes past weeks.
// @author       Christian B. B. Houmann
// @match        www.moodle.aau.dk/local/planning/calendar.php?fid=*
// @grant        none
// ==/UserScript==

window.addEventListener('load', function() {
    ClickSemesterButton();
    TogglePastWeeks(Toggle.hide);
    AddShowPastWeeksButton();
}, false);

let pastWeeks;
let pastWeeksShown;

const Toggle = {
    show: true,
    hide: false
}

function ClickSemesterButton() {
    document.querySelector(".fc-dayGridSemester-button").click();
}

function TogglePastWeeks(bToggle) {
    const WEEK_CLASS = ".fc-week";
    let allWeeks = document.querySelectorAll(WEEK_CLASS);

    pastWeeks = FindPastWeeks(allWeeks);

    pastWeeks.forEach(week => bToggle ? week.classList.remove("hidden") : week.classList.add("hidden"));
    pastWeeksShown = bToggle;
}

function FindPastWeeks(allWeeks) {
    const DAYS_IN_WEEK = 5;
    const PAST_CLASS_NAME = "fc-past";
    let pastWeeks = [];

    allWeeks.forEach(week => {
        // Traversing from week div -> div -> table -> tbody -> tr to get array of td
        let days = week.childNodes[0].childNodes[0].childNodes[0].childNodes[0].childNodes;
        let pastDayCounter = 0;

        days.forEach(day => {
            if (day.classList.contains(PAST_CLASS_NAME)) {
                pastDayCounter++;
            }
        });

        if (pastDayCounter >= DAYS_IN_WEEK) {
            pastWeeks.push(week);
        }
    });

    return pastWeeks;
}

function AddShowPastWeeksButton() {
    const fcRight = document.querySelector(".fc-right");
    const MOODLE_BUTTON_CLASSES = "fc-today-button fc-button fc-button-primary";

    const showPastWeeksButton = document.createElement("button");
    showPastWeeksButton.classList = MOODLE_BUTTON_CLASSES;
    showPastWeeksButton.innerText = "Toggle past weeks";

    showPastWeeksButton.addEventListener("click", () => {
        TogglePastWeeks(pastWeeksShown ? Toggle.hide : Toggle.show);
    })

    fcRight.appendChild(showPastWeeksButton);
}

Added a toggle button to show or hide past weeks.

Updated code for 1. refactoring and 2. more persistence in hiding columns.