I realize my previous post didn't apply to your assertion, since you obviously meant not that chrstian villagers in Israel were mixed with Greeks but that Greeks shared Jewish DNA. My apologies for the confusion.
Regardless of how "Jewish" Greeks and other ethnic groups may be, there is a Halakhic definition for Jewishness that they don't meet. And even considering that you don't consider this definition valid, I have already pointed out the fate of the original chrstian Jews makes it highly unlikely that today's Arab chrstians are in any sense whatsoever Jewish. This argument seems to me to be an attempt to delegitimize the Jewishness of Orthodox Jews and put the original Jewish chrstians (whom you insist survive in the person of Arab chrstians) in their place.
Again, please read some history on the original Jewish chrstians. Even right wing Catholic Malachi Martin admitted that they were lost to history and did not exist in any communal form whatsoever.