I don't understand what the pop-up blocker has to do with how Firefox renders a site. Very strange. Have you tried leaving the pop-up blocker on and just making an exception for the site? Or does that have the same problem?

More generally, Firefox has reduced support for Quirks mode sites over the years. You may need to use Internet Explorer 11 for sites from the pre-standards era.

Tried it. Did not help.

That's the problem. IE 11 does not like my customer. Only firefox, only hardcore.

Is there a public URL demonstrating the problem?

The problem is specific, associated with oracle products, famous for their bugs. Here it does not make sense. From the support of firefox I am looking to hear whether it is possible to switch the site in Quirks mode.

Firefox decides what rendering mode to use based on the page. I am not aware of any button or setting (such as a Compatibility View) to change that.

https://developer.mozilla.org/docs/Web/HTML/Quirks_Mode_and_Standards_Mode

You would probably use some proxy software (e.g. Privoxy or Proxomitron) to modify the html file and remove or change the DOCTYPE header to force quirks mode

Yes, the removal of the DOCTYPE helped. Thank you.

Dredlord said

Yes, the removal of the DOCTYPE helped. Thank you.