After doing some testing I've found that this issue is exclusive to 1.16.5. It's not my install, I tested it on another computer and had the same exact issue. Newer versions work fine.

Very strange, I can only reproduce it on 1.16.5 and 1.16.4 and I know this wasn't happening on these versions a month ago.
I'll try to figure out what's happening and how to get around it.

I know this wasn't happening on these versions a month ago.

It only became an issue sometime today. Minecraft launched perfectly fine yesterday and this morning.

I can still access multiplayer on 1.16.5 fabric but my friend can not on the same version

I can still access multiplayer on 1.16.5 fabric but my friend can not on the same version

Are you using an ely.by account while your friend is using an offline account? I noticed during my testing that ely.by accounts are unaffected by this.

Did you guys find a solution to this?

Using an ely.by account didn't fix the issue for me. What i did is to turn off the internet before launching my mc instance then turning it on right after i see the minecraft menu with all the buttons working :)

This seems to be an issue again; I was using an older version of the launcher, namely 6.3 so I could log into Ely.by directly. However, now that it's been replaced with the authlib-injector system, the multiplayer options in 1.16.4 and 1.16.5 are grayed out again. No amount of fiddling with the settings appears to work, the launcher logs in just fine and skins are fetched properly, but the game doesn't allow you to access the multiplayer features.

It looks like downgrading to 7.2 "fixes the issue" with the older ely.by implementation

So I messed around with the command line arguments, and it seems like not passing any of these makes 1.16.5 work fine, without the grayed out multiplayer options. I think it's due to authlib-injector already doing its job, but these come in erroneously and mess stuff up. I'll try to whip up a commit that includes a check for 1.16.4 and 1.16.5 that fixes this, for good.

-Dminecraft.api.auth.host
-Dminecraft.api.account.host
-Dminecraft.api.session.host
-Dminecraft.api.services.host