I need the 1.32 version to access a modded server but I encountered that Minecraft will crash with any version other than 1.33 (the last one) Is this due to something in the JCEF mirror server?

The MultiMC log just says:

[16:06:23] [Client thread/INFO] [MCEF]: Now initializing MCEF v1.32...
[16:06:23] [Client thread/INFO] [MCEF]: Selected mirror: ds58-mcef-mirror
[16:06:23] [Client thread/INFO] [MCEF]: Detected platform: mac64
[16:06:23] [Client thread/INFO] [MCEF]: Checking for missing resources...
[16:06:23] [Client thread/INFO] [MCEF]: Found 1 missing resources. Downloading...
[16:06:29] [Client thread/INFO] [MCEF]: Done; all resources were downloaded.
MacOS CEF Framework: /Applications/MultiMC.app/Data/instances/Project Rail V1.4/.minecraft/jcef/jcef_app.app/Contents/Java/../Frameworks/Chromium Embedded Framework.framework/Chromium Embedded Framework
[16:06:32] [Client thread/INFO] [MCEF]: Loaded 825 mime types
[16:06:32] [Client thread/INFO] [STDOUT]: [org.cef.CefApp:initialize:364]: initialize on Thread[Client thread,5,main] with library path /Applications/MultiMC.app/Data/instances/Project Rail V1.4/.minecraft/jcef/jcef_app.app/Contents/Java
Process crashed with exitcode 5 (0x5).

I don't believe this would be an issue with the JCEF mirror. However, you should try and convince the server owner to upgrade if possible.

Also, are you running an Apple Silicon Mac? If so, you must run Minecraft through Rosetta 2 (the default behavior from the vanilla launcher).

It's an intel iMac. What I finally did was to spoof the 1.33 version into 1.32 and building myself the jar. Then the server saw "1.32" and I could join without any further problems.

Closing the issue.