Netflix can have its bad moments.
I don’t think you said you cleared cookies in SF.
After doing so, close SF, wait 30 seconds, then start SF up again and try Netflix again.
A reboot of the computer would not hurt either.
You already can’t log in, so it can’t hurt to clear cookies.
Like others, it seems once I log into Netflix in SF, I stay logged in and almost never get asked to log in again unless I clear cookies and/or cache in SF.
If not, wait till later and try again. For me at this time I would wait till morn. as it’s almost 11pm