They can enter the priesthood / religious life if they don’t make a big show of the fact that they are gay
For holy orders, one must not practice homosexuality, present deep-seated homosexual tendencies or support the so-called “gay culture”.
For religions one must “be able to overcome their homosexual tendencies” an not maintain “that it is possible to adopt a third way”.
Vatican:**2. Homosexuality and the Ordained Ministry **
From the time of the Second Vatican Council until today, various Documents of the Magisterium, and especially the
Catechism of the Catholic Church, have confirmed the teaching of the Church on homosexuality. The *Catechism *distinguishes between homosexual acts and homosexual tendencies.
Regarding *acts, *it teaches that Sacred Scripture presents them as grave sins. The Tradition has constantly considered them as intrinsically immoral and contrary to the natural law. Consequently, under no circumstance can they be approved.
Deep-seated homosexual *tendencies, *which are found in a number of men and women, are also objectively disordered and, for those same people, often constitute a trial. Such persons must be accepted with respect and sensitivity. Every sign of unjust discrimination in their regard should be avoided. They are called to fulfill God’s will in their lives and to unite to the sacrifice of the Lord’s Cross the difficulties they may encounter
[8].
In the light of such teaching, this Dicastery, in accord with the Congregation for Divine Worship and the Discipline of the Sacraments, believes it necessary to state clearly that the Church, while profoundly respecting the persons in question
[9], cannot admit to the seminary or to holy orders those who practice homosexuality, present deep-seated homosexual tendencies or support the so-called “gay culture”
[10].
vatican.va/roman_curia/congregations/ccatheduc/documents/rc_con_ccatheduc_doc_20051104_istruzione_en.htmlD) SEXUALITY AND FORMATION 39. Today’s generations have often grown up in such integrated situations that boys and girls are not helped to know and appreciate their own respective wealth and limitations. Formation in this area is particularly important due to apostolic contacts of all kinds and the greater collaboration which has begun between religious men and religious women as well as present cultural currents. Early desegregation and close and frequent cooperation do not necessarily guarantee maturity in the relationships between the two sexes. It will therefore be necessary to take means to promote this maturity and to strengthen it with a view toward formation for the observance of perfect chastity.
Moreover, men and women must become aware of their specific place in the plan of God, of the unique contribution which respectively they should make to the work of salvation. Future religious should thus be offered the possibility of reflecting on the role of sexuality in the divine plan of creation and salvation.
In this context reasons must be given and understood to explain why those who do not seem to be able to overcome their homosexual tendencies, or who maintain that it is possible to adopt a third way, “living in an ambiguous state between celibacy and marriage” (104) must be dismissed from the religious life.
vatican.va/roman_curia/congregations/ccscrlife/documents/rc_con_ccscrlife_doc_02021990_directives-on-formation_en.html