Is it permissible to pray for unbaptized or non-Orthodox relatives, for example, those from the ROC? #

It is absolutely forbidden to submit commemorative notes for such individuals during the Proskomedia, that is, in the altar. During the Proskomedia and the Divine Liturgy, only the faithful—members of the Church—are commemorated. However, at home, you are free to decide for whom you pray, especially when it comes to your relatives. In church, you can request a moleben (intercessory prayer service) for such relatives.

The Apostle Paul writes:

“I say the truth in Christ, I lie not, my conscience also bearing me witness in the Holy Ghost, that I have great heaviness and continual sorrow in my heart. For I could wish that myself were accursed from Christ for my brethren, my kinsmen according to the flesh.”
(Romans 9:1–3)

The Apostle Paul was willing to be accursed from Christ for the sake of his fellow Israelites who did not accept Christ. It is indeed a great sorrow when relatives are not united with you in the one Church. Therefore, you not only may but are obligated to pray for them. Who else, besides you, will pray for them?

The same Apostle Paul writes to Timothy:

“But if any provide not for his own, and especially for those of his own house, he hath denied the faith, and is worse than an infidel.”
(1 Timothy 5:8)

What does it mean to “provide for one’s household”? It does not simply mean providing food and clothing. It primarily means caring for their spiritual salvation and desiring their eternal life with God. For this reason, you must pray for them, asking the Lord to soften their hearts. As long as a person is alive, there is hope that they may come to God. But how can they come to God if you refuse to pray for them?

“For what knowest thou, O wife, whether thou shalt save thy husband? Or how knowest thou, O man, whether thou shalt save thy wife?”
(1 Corinthians 7:16)

This refers to a Christian woman with an unbelieving husband, and a brother with an unbelieving wife.

The Apostle Paul also recommends praying not only for relatives but for the entire world:

“I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; for kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.”
(1 Timothy 2:1–2)

At the time, kings and those in authority were pagans.

The same applies to the deceased. To God, all are alive. Therefore, you must also care for the deceased, who can no longer pray or give alms for themselves. They await your prayers. However, the form of prayer differs. In church, you cannot submit notes for the altar for those who are not members of the Church. If they were not baptized, they were not given a Christian name, and thus the Church does not commemorate them by name. In such cases, you can give alms on their behalf and ask for prayers for the deceased relative, such as through the canon to the martyr Varus. You can also pray to the Lord or the Mother of God without naming the individual. God knows for whom you are praying.

— Priest Evgeny Gureev