JSFiddle - React, Tailwind, and code Playground
HTML
<h1>Abra o console para ver o output.</h1>
JavaScript
var str = "div.classe1{background:red}.classe2 div a{background:#00f}.classe3.classe4{background:green}.classe5{background:#ff0}",
achados = str.match('\.(-?[_a-zA-Z]+[_a-zA-Z0-9-]*)(?![^\{]*\})');
console.log(achados);