[pharmamom]

And would I be correct in understanding that the reason fellowship is "impaired" is because we can't be in communion with those who do not share our faith; i.e., do not believe what we believe?

[Kolokotronis]

In great measure yes,

"+Chrysostomos loudly declares not only heretics, but also those who have communion with them, to be enemies of God." St. Theodore the Studite, Epistle of Abbot Theophilus

or

"As for all those who pretend to confess the sound Orthodox Faith, but are in communion with people who hold a different opinion, if they are forewarned and still remain stubborn, you must not only not be in communion with them, but you must not even call them brothers." St. Basil the Great