As ChrisW said, there are numerous examples of humor and irreverence in Zen lore.
However, unlike most of the jokes about e.g. Christianity which are often said without a wholesome purpose, or sometimes with the objective of pointing out an inconsistency in Christian declared values vs. practice, in Buddhism all activities, including jokes, are 100% subordinated to the primary goal.
Before you can understand the role of jokes in Zen Buddhism, you should understand the crucial role of attachments as obstacles to enlightenment. (I think you are very close to this already, since you have a natural antipathy to superstitions, unexamined beliefs, and rigid/stubborn adherence to subjective points of view & philosophical abstractions.)
While I can't give justice to this topic in one short answer, the idea is that attachments both bias the mind off an ideal objective basis AND lead onto dangerous and often harmful pursuits AND constitute the necessary condition of suffering due to a mismatch between "how is" and "how should be" (the target of attachment).
The traditional Buddhist device against an attachment is known as an antidote. Often antidote takes form of an object opposite to the target of attachment. For example, when attachment is to sexual pleasures, the antidote is contemplation of decomposing corpses. When attachment is to negative attitude towards society, the antidote is generation of loving-kindness, etc. Which leads us to the role of humor as an antidote to attachment to ... the very Buddha Dharma itself.
So for example, if a Zen master notices that his student lost his fundamental sanity and has "gotten drunk on the shravaka wine" to use Dogen's parable, he might offer a following piece of wisdom:
A monk once asked Ummon, "What is the Buddha?"
"A dried shit-stick!" -- was the answer.
Last night, this mountain monk [Dogen] unintentionally stepped on a dried turd and it jumped up and covered heaven and earth. This mountain monk unintentionally stepped on it again, and it introduced itself, saying, "My name is Shakyamuni."
Bodhi and Nirvana are poles for tying up donkeys.
If you meet the Buddha on the road, kill him!
Do you understand? Buddha-dharma is medicine for suffering caused by ignorance and attachment, including both intellectual ignorance and attachment, and emotional ignorance and attachment. There are very many different forms of delusion and attachment. Buddha said there are 84000 kinds! A particular form of medicine works better for a particular form of disease. Buddhist humor is one of such medicines.