Certain teachings, like The Real Presence of Christ in the Eucharist, The Holy Trinity, The Immaculate Conception, that the Pope is the successor to St. Peter, that every Bishop in the Church can be traced back to Jesus’s Disciples (Apostolic Succession) and many other doctrines are considered core teachings—these are considered absolutely settled Dogma and essential to the Catholic Faith.
Some things are not essentials of the Faith. For example, Priestly Celibacy is a discipline, not a Dogma and can be changed without changing any of the core teachings of the Catholic Church. Priests were not always required to be celibate. There are a minority of Latin Rite Priests that are married (Usually these were High Church Protestant Ministers who converted and became Priests). In Catholicism, there are actually 24 Churches—the Roman Catholic Church being by far the largest. But there are Eastern Rite Catholic Churches that have their own Rites. In many of these Churches, Priests can be married (I am pretty sure in all of these Churches they cannot get married after they are Ordained though, much like the Eastern Orthodox Priests)