You're mixing up political and epistemological obligations. Politically, in liberal societies at least, we're free to believe whatever we want as long as those beliefs don't tend to cause others harm. But the burden of proof issue is part of epistemology, the study of knowledge. Epistemically, if we're interested in philosophically justifying our beliefs, we have the obligation to use reason and to base our beliefs on evidence and good arguments. These obligations merge with ethics since we're obliged also not to deceive or to manipulate others, and so on.

The problem with saying that atheists have an equal epistemic burden of proof is that it's impossible to prove a universal negative. But that doesn't mean we should believe there are unicorns or goblins or spaghetti monsters just because we can't absolutely disprove these things by inspecting every corner of the universe. This is why the epistemic burden falls more to the one who makes the positive claim, not to the one who's just listening to it.

Note the similarity with courts of law: the epistemic burden falls to the prosecution that alleges that someone committed a crime, not to the defense attorney.