That's hard to quantify. What I can tell you is that Tor with TBB in its default configuration is the safest and most anonymous way to access clearnet sites, of all the options available on the Internet. Accessing hidden services is safer than clearnet sites. Some argue that Freenet is safer than hidden services, but I have reservations about using Freenet and I2P because they are so small. It's easier to enumerate all IP addresses, and I'd rather not have my IP on some list, even if they can't prove what I'm doing. I'd rather mix in with the millions of Tor users and access hidden services instead. From simply logging into the site? Assuming you don't provide identifying info, that alone won't deanonymize you. Again, there would have to be some specific attack, like the adversary tricking you into running malware, or selecting his relays for entry guards.