The push behind the non-denominational priests of becoming Catholic has been pushed by their organizations allowing exactly that, married priests, homosexual priests, women priests, etc.
These, for example Anglican priests who were already married left and became Catholic, and were formed through to be Catholic priests.
They left to become Catholic because of the disarray in their own church.
Nevertheless, various requests about possible admission into the Catholic Church were made to Catholic bishops in the United States, who in turn contacted the Holy Father. In response, Pope John Paul II, through the Sacred Congregation for the Doctrine of the Faith, issued a clear although brief statement in June 1980.
First, the Holy See admitted allowing a "pastoral provision," which would provide "a common identity reflecting certain elements of their own heritage." Here an entire Episcopalian congregation could enter the Catholic Church and be allowed to remain a parish and use an Anglican-style Catholic Mass with either the traditional language of Archbishop Cranmer's <Book of Common Prayer> or the modern English version.