I don't think that sounds odd at all. Most of us are bi-ritual by necessity. I think the concern is with spiritual formation - what we do primarily is one rite (at home prayers) as each cursus of a liturgical tradition was developed so that it trains the Christian who follows it. So - I'm Western rite normally, but often participate in both Arabo-Byzantine, Helleno-Byzantine, and Slavo-Byzantine worship (and, there is enough difference between those, so that going from Greek to Slavic is surely 'bi-ritual'.) Even more with the Old Rite such as they have in Erie, PA - which is very beautiful. Otherwise, I think the whole paradigm of the rites being different enough so to require a term 'bi-ritual' is more native to late Roman Catholic thought, and not really part of our Orthodox understanding of worship. An Orthodox Christian simply in the worship of the local church - it is all the Orthodox ritual (whether Chrysostoma, Gregorian, etc.) In the Russian Church, we have had clergy serving multiple rites for the past two centuries - but without the idea that they were 'bi-ritual' (sometimes we say so as a concession to weakness) - a Russian Orthodox priest simply celebrates those rites of the Russian church: whether the New Rite, Old Rite, or Western rite (all have been approved by the Holy Synod.)
I have a friend who is always asking, "what's the point?" I think if one is focused on that, the rest will take care of itself.
What about the ancient wisdom of just adopting the rite particular to where you happen to be worshiping? A particular rite is the expression of the faith, but the western and eastern rites were happy to co-exist for centuries sharing in the same faith.
Wow...I wasn't even aware that this would be an issue. I'm a total newbie though, I just became a catechumen a couple of weeks ago....our church (Ukrainian) doesn't have a building, so when we can't get the usual room so services are cancelled, I plan on going to an Antiochian church near my parents house. I figured as long as I go to services on Sunday, and follow the prayer rule the priest gave me at home...is there more than this I need to think about? Also, why does it matter which church you attend? I don't mean hopping aorund all the time so that you don't get to know the people and the priest at one place regularly, but... I mean, if I moved, and the closest church was Greek Orthodox, would it be better for me to drive out to find Ukrainian one instead? Sorry if I seem very ignorant with my questions.