I agree with your reasoning, but I think there are plenty of reasons to be unhappy about religion that go beyond the absence of a preferred state.

In other words, I think I should be actively displeased that religion exists and is prevalent, not merely being non-happy. Neutrality is included in non-happiness, and if the word were used logically, unhappiness. But the way it's actually used, 'unhappy' means active displeasure.