I think a person who is knowledgeable and secure in his faith can use their own prudent judgement on this matter. Once in a while (maybe several times a year) I will go to a friend's Evangelical service or my father's Baptist service, and I will certainly pray with the congregation, who are brethren in the sense of being baptized Christians. However, when I hear something not in accord with the Catholic faith, I will abstain (of course, the most predictable area is communion time---no little cups of grape juice and cracker packets for me---but sometimes I will not pray the prayer offered by the minister or sing a hymn sung by the congregation if it is problematic).
As far as I can remember, I can't think of a time where I needed to "abstain" at an Orthodox Divine Liturgy (except for Communion, of course).