I made a tampermonkey script for this:
https://gist.github.com/rchernobelskiy/d8c71e6e1ebcdd22cf897ad28da875a3
Re-pasting here if easier:
// ==UserScript==
// @name Slack tab title asterisk remover
// @namespace http://roman.chernobelskiy/
// @version 0.1
// @description Permanently keeps the asterisk out of slack's tab title.
// @author Roman Chernobelskiy
// @match https://app.slack.com/*
// @grant none
// ==/UserScript==
(function() {
'use strict';
new MutationObserver(function() {
if(document.title.indexOf('*') != -1) document.title = document.title.replace('*', '');
}).observe(document.querySelector('title'), {
subtree: true,
characterData: true,
childList: true
});
})();