(Posting this for anyone who may face similar issues...)
So, I was trying to login to the main https://codeforces.com/ website since yesterday but couldn't log in. Every time I tried to log in, it was showing me the HTTP 403 error saying access forbidden. Afterwards, I tried logging in to one of the mirror sites http://m1.codeforces.com/ and it worked. Seemed like, there were some cookie related problems. So I just cleared the cookies and tried to login again, and this time it worked! Not sure why it happened, this is the first time I've seen it.
In case you don't know how to clear the cookies (showing it for chrome, should be similar for other browsers), click on the lock icon in the address bar and then click Remove for all the cookies. This should solve the problem.