You have something that is MITM'ing security certs. What security software do you use? It's likely because Firefox 61 supports TLS 1.3, and a lot of ancient security software (or security software that does terrible things like HTTPS scanning, which is just disguised stealing of your internet data) doesn't properly implement TLS 1.3.

You should check what's happening with your network.

Hi richardmarchesi, is this a new issue in Firefox 61 or Firefox 60? What was the last version of Firefox that worked normally with your company's proxy server?

Normal Issues

As you probably know, a proxy server sets up as a "man in the middle" of browsing connections. For HTTPS, the proxy needs to generate fake website certificates to fool your browsers into connecting, and Firefox naturally won't accept them until it is properly set up.

By default, Firefox uses a separate certificate store (cert9.db file) for each profile. Other browsers use the Windows certificate store. I suspect your IT automatically sets up the proxy's signing certificate as a trusted authority in the Windows certificate store, but doesn't have a mechanism in place to do that in Firefox.

New Issues

See Tyler's reply regarding a potential new compatibility issue in Firefox 60 and later.