The readings should be proclaimed by those baptised.
There is a clear indication of this in the liturigical book “Rite of Christian Initiation of Adults” n. 87:
“One or more readings from Scripture, chosen for their relevance to the formation of the catechumens, are proclaimed by a baptized member of the community.”
(From The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 74).
It is talking about a “Celebration of the Word of God”, rather than the readings at Mass. But if a catechumen should not do the readings for a “Celebration of the Word of God” then it applies even more so for the readings at Mass.
It seems to me that proclaiming the readings is a teaching role. Being a catechumen is the role of a student.
Regarding those who are baptised, but not Catholic there are instructions from the The Directory for the Application of Principles and Norms on Ecumenism at
vatican.va/roman_curia/pontifical_councils/chrstuni/documents/rc_pc_chrstuni_doc_25031993_principles-and-norms-on-ecumenism_en.html :
For Eastern Christians it has:
“126. Catholics may read lessons at a sacramental liturgical celebration in the Eastern Churches if they are invited to do so. An Eastern Christian may be invited to read the lessons at similar services in Catholic churches.”
Then for “Christians of Other Churches and Ecclesial Communities” it has:
“133. The reading of Scripture during a Eucharistic celebration in the Catholic Church is to be done by members of that Church. On exceptional occasions and for a just cause, the Bishop of the diocese may permit a member of another Church or ecclesial Community to take on the task of reader.”