What did mystery religions, like the cult of dionysus and the cult of isis, have in common with stoicism and epicureanism?

Because both religions have in their core the seek of happiness and the proposition to not care about the problems, to live the moment with pleasure. These ideas are in communion with the Stoicism and Epicureanism beliefs.

Explanation:

Epicureanism and the Stoicism seek the ataraxia, or in other words, the absence of worries. Even if they understand this term in different ways, their core is built around this idea. When we apply this conception to religious cults such as the Dionysus and Isis, and we look closely at their notion about life, to live the moment, to care about the happiness, and to enjoy everything closer to you, then we see similarities with these Greek philosophies.