NB: I haven't read the entire thread (only the OP and this page), and I'm Oriental Orthodox, not Eastern Orthodox.
But I was Roman Catholic before converting, and when I was still in the RC people there often joked about an "ABC Christian" mentality among some Protestants -- "Anything But Catholic". I would imagine the same follows the Eastern Orthodox (my own communion is usually either not included/known, or is included by default) due to ignorance which focuses on external similarities only -- "these people dress up and wear funny hats and maybe even chant in a language I don't understand...sounds
Catholic-ish to me!"
Basically, everything's the same if you're already convinced that it is, so it's not about the actual beliefs, but about what seems to be the case to the outsider. Sadly, even getting them to liturgy might not help, depending on the type of person you're dealing with (though it's still worth it to try, I think, because sometimes
repeated exposure will cause something to click), because it could just confirm that "Yes, these people are weird and it looks, smells, and sounds like I thought it would;
mission accomplished -- I found the Rome-ish pagans!"
God forbid you tell them you actually
do have a Pope, as I believe you guys also honor your Alexandrian Patriarch with that title (please correct me if I'm wrong about that; if I recall correctly, I read that on this very board). Then you'd have to get into early Alexandrian Christian history, and maybe even talk about the Patriarch of Alexandria as the "Judge of the Universe" (my favorite title for any bishop, by far) and things like that, all to explain how and why the Pope of Alexandria is not akin to the Pope of Rome in his claims to authority, theology, etc. Fun times, surely. I know
I never tire of that, as a Coptic Orthodox person.