Some problems occur when your Internet security program was set to trust the previous version of Firefox, but no longer recognizes your updated version as trusted. Now how to fix the problem: To allow Firefox to connect to the Internet again;

• Make sure your Internet security software is up-to-date (i.e. you are running the latest version).
• Remove Firefox from your program's list of trusted or recognized programs. For detailed instructions, see

Configure firewalls so that Firefox can access the Internet. {web link}

I'm not seeing that serious issues reported for MacOS 11.

• Bug 1648487 - [meta][11.0] Investigate compatibility with macOS 11.0 Big Sur

(please do not comment in bug reports
https://bugzilla.mozilla.org/page.cgi?id=etiquette.html)

You can create a new profile as a quick test to see if your current profile is causing the problem.

See "Creating a profile":

• https://support.mozilla.org/en-US/kb/profile-manager-create-remove-switch-firefox-profiles

If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.

• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile