Rumi was the son of a very popular Sufi, he probably grew up exposed to Sufism at a very young age. Sufism is a branch of Islam that focuses on developing inner character. Rumi and his father both did not agree with some of the legal and ritual practices that many were blindly following. He encourged people to go and experience life and to not blindly follow the religious leaders of the day.
An interesting topic that I wanted to touch on was his involvement in Sufi whirling. Also known as whirling dervishes, they dance for meditation and to show praise. Below is a quote from PBS that best describes Sufism and the whirling dervishes.
"Sufism, the mystical branch of Islam, emphasizes universal love, peace, acceptance of various spiritual paths and a mystical union with the divine. It is associated with the dancing of whirling dervishes, who originated in the 13th century as followers of the poet and Muslim mystic, Rumi. Their dance is a traditional form of Sufi worship, a continuous twirling with one hand pointed upward reaching for the divine and the other hand pointed toward the ground."