Catholics are only permitted to pray for those who die as Catholics
St. Augustine, Sermon 172, 5th century: “There can be no doubt at all that these things [i.e. prayers] are of value to the departed; but to such of them as lived in such a way before they died, as would enable them to profit from these things after death. For those, you see, who have departed from their bodies without the faith that works through love (Gal 5:6) and its sacraments, acts of piety of this sort are performed in vain.”
Pope Gregory XVI, Officium, Feb. 16, 1842:
“But this is the report given to us concerning the Catholic rites used in her [Queen Caroline’s] funeral; and we have before our eyes your letter, which, on the 19th day of November, you had given your parish priests regarding this matter. But hardly are we able to express in words what kind of mental anguish we experienced when we learned from the reading of the same [letter] that you had commanded that those public supplications which have been instituted by the Church for all who die in Christian and Catholic fellowship should be held on this occasion for a woman ruler who met her ultimate end in the same heresy wherein she had most manifestly lived.
Nor has it any bearing on the matter whether in the final moments of her life she may have been enlightened to repentance by a hidden benefit of the merciful God. For, as a matter of fact, these more secret mysteries of divine grace in no way pertain to the exterior judgment of ecclesiastical authority; and this is why it has been forbidden by the ancient as well as the recent discipline of the Church for men who die in the external and notorious profession of heresies to be honored with Catholic rites.
And yet it was not enough for you to prescribe Catholic rites on this occasion; no, you even commanded that in his funeral eulogy for the deceased the sacred speaker should specifically commend her to the pious prayers of the faithful, and you forbade him to add anything further to explain the difference between that funeral and the funerals of Catholics. Indeed, at the beginning of your letter, you did not fear to speak about her death as to say that she had been called by God from this world into eternal life.
We certainly do not see how what was so boldly affirmed by you even with no clarification added can be truly reconciled with the Catholic dogma concerning the necessity of the true Catholic faith to obtain salvation – with that very dogma, We say, which, among other principal articles, has been reproduced in the formulas for the profession of the faith, and which We also commended in Our encyclical letter to the bishops of Bavaria to be observed as the antidote to the spreading pest of indifferentism, an antidote especially necessary at this time.” (Acta Greg. XVI, Vol. III, pp. 198-199)
There are some very interesting statements in this letter. First, Pope Gregory XVI rebukes the bishop and reaffirms the Church’s teaching that people who die outside of communion with the Catholic Church cannot be honored with Catholic rites. This law goes back to the ancient Church. It is summed up as: “With those with whom we have not communicated while they were living we do not venture to communicate with while they are dead”. This was taught by Pope St. Leo the Great, Pope St. Gregory VII, and others.
Sources:
Augustine: Only Pray For Deceased Catholics
No Latin Mass Or Prayers For Dead Non-Catholics …