No. Ho'oponopono is a Hawaiian term that means "to correct errors." Dr. Reese describes it as more science than spiritual as we are simply being mindful of our thoughts and emotions and taking full responsibility. This helps us stay in the present moment while cleaning out our junk that we have repressed for years and years.
While this practice isn't religious, Kevin, likes to draw on spiritual figures such as Jesus, Buddha, Rumi, Osho, Ramana Maharshi or his mentor, Vishrant. However, they're meant to be examples. Having belief or "following a religion" isn't involved in Ho'oponopono.
Kind of like AA, the idea is there is a divine force/source that is involved in our existence. Many people call it GOD. That's it. A higher power is all that's needed for this practice. Your religion is irrelevant.