Here we go again, lol. Reading comprehension is your friend. They do not claim to be Orthodox, although there is quite a bit of contact between the Orthodox and themselves now, and has been since the fall of the Soviet Union and Eastern Bloc satellite states.
The historical claim is that the people were originally proselytised by Cyril and Methodius who were from the East, both geographically speaking and theologically, before there was any schism between East and West. These people fell under Roman authority by the sword and several aspects of their church, faithfully honored and followed since the times of Cyril and Methodius, were then taken from them by the Roman church which had acquired several novel practices since then, which would be where the controversy regarding the Bible in the vernacular and mass in the vernacular entered into this discussion.
This led to long-simmering offense and resentments, ultimately leading to Jan Hus and the Hussites who broke with Rome outright in order to return their church to the practices originally taught them by missionaries from the East.
In this sense, the Moravian Church has roots much more in the Eastern Orthodox. Their protest such as it was, was due to a desire to return to Orthodoxy, which was being prohibited by the Roman church.
Do you understand now?
“They do not claim to be Orthodox”
Then we can dispense of their claim to be Orthodox or connected to them.