User script which can be used with TamperMonkey and similar browser extensions.

remove-youtube-scrollbar.js

// ==UserScript==
// @name          YouTube Remove Themed Scrollbar
// @version       1.0.1
// @description   This script removes the themed YT-scrollbar one second after load.
// @author        Julian Weinert
// @run-at        document-start
// @match         *://*.youtube.com/*
// @match         *://*.youtu.be/*
// @updateURL     https://gist.githubusercontent.com/julian-weinert/425fa15d7117785e84cad6fbf8df460c/raw/remove-youtube-scrollbar.js
// ==/UserScript==

function wrapSetAttribute(a) {
    a._setAttribute = a.setAttribute;
    a.setAttribute = function(attr) {
        if (attr.includes('scrollbar')) {
            return;
        }
        a._setAttribute(...arguments);
    }
    
    var attrs = [...a.attributes];
    attrs.forEach(attr => {
        if (attr.nodeName.includes('scrollbar')) {
            a.removeAttribute(attr.nodeName);
        }
    });
}

wrapSetAttribute(document.documentElement);
wrapSetAttribute(document.body);