And he is an Orthodox (just that) as καθολική χριστιανή in the other example (the one of the friend from Italy) only accepts Catholic and not Christian Catholic? I know there are differences within Orthodoxy as there are in Catholicism, but it can be understood as a general statement... (I think)
I'm afraid I can't say I see your point here.
Firstly, what was the other question? You'll have to be a bit more specific than that.
Secondly, I'll guess what you're saying is that, Catholic was an accepted translation in the other sentence, all by itself while here, Christian is needed. I guess that's because, as you can see here https://en.wikipedia.org/wiki/Orthodox , this term is being used for other religions as well.
I answered "He is an Orthodox" and this was considered wrong. For the similar question in the same group of questions I answered "He is a Catholic Christian" and it was consider wrong by Duolingo and correction was: He is a Catholic.
There should be some logic and coherence in the system of Duolingo. Please, correct this part.
In English (I'm British English) it sounds a little rude to use the indefinite article, we're more likely to turn the religion into an adjective. Meaning, we'd be more likely to say "She is Catholic" than "She is a Catholic", more likely to say "he's muslim" than "he's a muslim" etc. There's a sense that when you say someone is a someone, it can come over as potentially confrontational or unpleasant. So I translated this as "He is Orthodox Christian." which was marked wrong. I can understand why, because it does have a different literal sense to the sentence in Greek. My question is (sorry for long preamble): does the same sensitivity occur in Greek at all? Would we be more likely to say "είναι ορθόδοξος χριστιανός" or is it just not an issue in Greek?