Therefore, we humbly pray and beseech Thee, most merciful Father, through Jesus Christ Thy Son, Our Lord, to receive and to bless these (+) gifts, these (+) presents, these (+) holy unspotted sacrifices, which we offer up to Thee, in the first place, for Thy holy Catholic Church, that it may please Thee to grant her peace, to guard, unite, and guide her, throughout the world: as also for Thy servant N., our Pope, and N., our Bishop, and for all who are orthodox in belief and who profess the Catholic and apostolic faith.

It follows from this that the prayer is not offered for those who are not orthodox in belief.  The mere profession does not suffice in this instance.  They must truly believe all Catholic doctrine in order to benefit from this holy prayer of the Mass.  Additionally, the parallel prayer of the Novus Ordo lacks the necessary humility in order to render it efficacious.  Additionally, it appears, following the prayers in comparison with the old, that the N.O. offers mere bread and wine for the Pope, clergy and the entire Church.