My desktop browser (Firefox and Chrome) on Linux just shows me a perpetual spinner icon when I click login. I had the same problem when I tried to sign up. My current work around is to access Lemmy on mobile only.
I had this problem at first, I believe when my registration was waiting for approval. Later in the day I cleared browser cache, and it just seemed to work.
I've noticed something interesting. My account was created on my laptop. Logging in there is fine. From the phone, with the spell checker on, the phone brings up my username. If I click on it, it enters my username into the username box, BUT WITH AN EXTRA TRAILING SPACE. I'll get an infinite spin if I use it as is, but can log in if I remove the trailing space first.