Praying for non orthodox is allowed, but the Divine Liturgy is only for members of Church, that is only for Orthodox. Among other reasons, this is also for respecting non-orthodox's freedom to remain non-orthodox.
God respects freedom of non-orthodox, so we also do the same. For if we bring them into Devine Liturgy against their expressed will, we offer no service to them.
"Priest: Among the first, remember, O Lord, his Beatitude, Metropolitan ______, his Grace, our Bishop ______, and grant them to Your holy church in peace, safety, honor, and health, and many years rightly teaching the word of Your truth.
People: And all mankind."
Or how about:
"Deacon: For the President and all civil authorities of this country, and for those serving in its Armed Forces, let us pray to the Lord.
People: Lord, have mercy."
And as far as respecting others' freedom: I really don't see what that has to do with not praying for them in the liturgy?
Edited by John S., 23 May 2016 - 03:29 PM.