Is it permissible to follow the trivial posts of atheists with the intention of ridiculing their way of thinking, knowing that this does not affect one's sound belief?

It is not permissible to enter websites containing doubts, even with the intention of mockery, because that may be among the steps of Satan by which he entraps a person. The Sharia has commanded avoiding doubts, as the Prophet, peace and blessings be upon him, said: "Whoever hears about the Dajjal, let him keep far away from him. For by Allah, a man will come to him thinking he is a believer, and then follow him due to the doubts he sends forth." So, beware of falling into Satan's snares.