it may even affect the efficiency of gifts (with Rome i find gifts to Greek minors (same religious group) tend to be very effective though it is possible that the strength of Rome may be part of it).
I think you might be right. Despite my horrible failures of gift-giving to the Syracusans, when I later gave gifts to the Palmyrans, who share my culture and religion, I got relation boosts of +20, +22, and +40. It seems that you get more out of gifts if you have more in common with the faction you're giving them too.
Of course, gameplay-wise, this isn't that helpful. Obviously, one is trying to give gifts to people that normally aren't friendly to you, not people who share your culture and religion and are thus often quite friendly already.