Did you look here if this works from Mozilla archive?

https://archive.mozilla.org/pub/firefox/releases/133.0.3/

Sorry, the last version of Firefox that will work on your version of MacOS is the Extended Support Release of Firefox 78 (see: Firefox Mac OS X 10.9, 10.10 and 10.11 users move to Extended Support Release). I think that's the one you already have.

What site is telling you that you need to update?

If you are referring to an email from Mozilla that circulate last Spring about updating if you want to continue using Sync, basically, you would need to update Mac OS first.

Did you look here if this works from Mozilla archive? https://archive.mozilla.org/pub/firefox/releases/133.0.3/

This is a macOS 10.11 user and Firefox since 116.0 including the current 133.0.3 requires macOS 10.15 (ten.fifteen) at minimum to run so it will not work. As stated above the old 78.15.0esr was the last to support macOS 10.11.

Hi, I use MAC OS X 10.11.6 EL CAPITAN. It's doesn't accept the new Firefox. So what can I do? How can I make this new update????

If you do upgrade to macOS 10.12 then you can download the Firefox 115.18.0esr.dmg at https://archive.mozilla.org/pub/firefox/releases/115.18.0esr/mac/ (will not run on your macOS 10.11.6)