Focusing on the Christian religion, I would like to receive specific information about monastic movements (the Franciscan Order more precisely) that show that there are various expressions even within the one religion and that, in addition, there are other forms of religious movements that seem to share the intention of changing society and even the world.

The Franciscan Order, the largest order within the Catholic church, was founded by St. Francis of Assisi in 1209. Within the order, there are three orders. The First Order consists of priests and laymen who practice preaching, penance, and prayer. Within this order is the Friars Minor (O.F.M.), the Friars Minor Conventual (O.F.M. Conv.), and the Friars Minor Capuchin (O.F.M. Cap.). The second order is made up of nuns who are called Poor Clares in the Order of St. Clare (O.S.C.). Lay people make up the third order, and they try to practice the ways of St. Francis through prayer, teaching, and charity. St. Francis was born wealthy but gave up all forms of luxury and connections with his family to live with fellow believers. He wore an unadorned tunic and chose this simple form of clothing for his followers.
St. Francis went to Rome in 1209 to receive a blessing from Pope Innocent III to establish an order. Members of his order owned no possessions, either individually or in common, and they traveled about working with the poor and sick. They could accept food for their work but not money of any kind. They lived in church properties. St. Clare established the Franciscan nuns in 1212 in Assisi, and the nuns lived their lives in poverty. Franciscans came to the New World in 1493 with Columbus, and they were active in the colonial period in areas such as Florida, New Mexico, and California (Junipero Serra arrived in San Diego in 1769). Different parts of the order were also active in French Canada and in Maryland. The Franciscans show that even within Catholicism, there is a diversity of movements that try to change the world in different ways; the Franciscans were founded on the idea of dedication to helping the sick and the poor.
https://usfranciscans.org/