score:8
Okay, for the purpose of providing an answer, I've gone to this site:
http://www.antiochian.org/whatorthodoxbelieve
which, correct me if I'm wrong, seems to present the views of the Eastern Orthodox church, from their POV.
The only thing I can see as being a problem, would be the phrase, taken a bit out of context from Timothy:
"From such withdraw yourself' (1 Timothy 6:5).
said to refer to cults. The actual passage (KJV) is:
Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself.
Obviously, it is up to the person doing the interpreting as to whether or not Buddhism is "destitute of the truth", and whether that would then be enough to require you to "withdraw thyself".
Either way, your question is actually about strategy, so, given the assumption that you don't really care what the church has to say as long as you aren't subject to their censure, I imagine it would be enough to just not speak about it to them. I don't assume you'd be found out otherwise.
It's really the best, I think; speech that is unpleasant, e.g. telling a devout Christian that you are participating in what they view as a cult, should only be delivered with care. (See the Abhaya Sutta, MN 58, for a discussion of unpleasant speech).
So, td;lr: unless you think you can convince your fellow Christians that you are not really committing sin by participating in Buddhism, best would be to just avoid mentioning it. Or, you know, leave Christianity and become Buddhist ;)