JSFiddle - React, Tailwind, and code Playground

HTML

<button id="upload_widget" class="cloudinary-button" style="background-color:red">Upload files</button>

<script src="https://widget.cloudinary.com/v2.0/global/all.js" type="text/javascript"></script>  
<style>
.cloudinary_fileupload {
  background-color: "red" !important;
}
</style>
<script type="text/javascript">  
var myWidget = cloudinary.openUploadWidget({
  cloudName: "demo", uploadPreset: "preset1",
  sources: [ 'local', 'url', 'dropbox','facebook'],  
 styles:{
    palette: {
      window: "#FFF",
      windowBorder: "#90A0B3",
      tabIcon: "#0E2F5A",
      menuIcons: "#5A616A",
      textDark: "#000000",
      textLight: "#FFFFFF",
      link:  "#0078FF",
      action:  "#FF620C",
      inactiveTabIcon: "#0E2F5A",
      error: "#F44235",
      inProgress: "#0078FF",
      complete: "#20B832",
      sourceBg: "red"
    },
    fonts: {
        "'Cute Font', cursive": "https://fonts.googleapis.com/css?family=Cute+Font",
    }}
  }, (error, result) => { });

document.getElementById("upload_widget").addEventListener("click", function(){
    myWidget.open();
    document.getElemementByClassName('css-anf0i3 BUTTON outline-0 flex-nowrap items-center justify-center pointer fw6 bg-link bg-link-c').style['background-color'] = 'orange'
  }, false);
</script>