None of the theme settings or otherwise are likely culprits.
There’s JS involved in the functionality so something has to be circumventing that or there’s a JS error occurring. I’m unable to duplicate the issue myself so I need more information to know what’s actually going on.
If you’re comfortable with me accessing the admin panel of your site you could give me a temporary login/pass.
My email address is:
jamie AT methnen.com
If not I need a lot more detail.
1. Can you see any errors in the browser console after clicking the Select File button? There’s some good directions on how to see your console here: https://balsamiq.com/support/faqs/browserconsole/
2. You mention both Chrome and Firefox, what operation system though? Windows? Mac? Linux? Etc…
3. Any browser extensions that you have active across both browsers? Ad blockers perhaps? I’ve seen those occasionally get to aggressive and block legitimate code.
4. Any other details you might be able to provide.