Do you personally feel more safe, or better, whatever the adjective you want to use would be... about logging in to a remote server that uses software you can read the source for versus software you can't read the source for?
It seems like a sticky problem because even if Freenode purports to be open, and you can read the source code of what software they say they use, you can't actually see the source code powering their service, right? Like you can't just SSH to the boxes, and look at the source and say "ok, they haven't messed with anything, so I'm ok signing into their servers".
Like, you could see the very JavaScript running in your browser. You downloaded it, it's running locally. You can't see the backend, though. You can't tell how your data is being used. That's the thing that feels scarier to me, although admittedly, I use plenty of services based on closed source software as well as open source software, and it doesn't really give me too much pause.
I guess I just don't really understand the fervor around the "openness" aspect if you're not actually the one running the service. You're still at the mercy of a service operator who could be eroding the "freedom" you think you have.