Considering that their national flag has 5 crosses, which resemble the crosses said to be used by the Crusaders, I'd say not very.
“South Ossetia is part of Georgia only because the Georgian communist Stalin said it was. There is no shared language or culture. IN the past Ossetian Christians have always looked to Russia for protection from muslim hordes.”
How muslim is the rest of Georgia?
12% -— 640 thousand according to wiki
The return to Christian symbols and somewhat of an influence has apparently troubled some...but they aren’t making noises yet.
Considering that their national flag has 5 crosses, which resemble the crosses said to be used by the Crusaders, I'd say not very.