Armenians became Christian in the 4th century AD when the Kingdom of Armenia was converted to Christianity. Kurds during this time neither had a state nor were attested at all in records, in fact we only hear the name 'Kurd' until after the Islamic invasion.

The 4th cenutry in particular was a great defining period for the kingdom of Armenia as it took on its own alphabet and direct translation of the bible into the language. The century after saw it reject the Council of Chalcedon in 451 which split it from the Roman church definitively.

Interestingly, in the same year, Armenian Christians managed to prevent conversion of the Armenia (which was part of the Persian Sassanid empire at this time) to the imperial Zoroastrian religion, in the Battle of Avarayr which to day is the most important battle in Armenian nationalism and is celebrated in the holiday of Vartanantz (after the commander Vartan Mamkionian).

It was during this period that Armenia took on its own Christian character, separate from the Persians that ruled it and from the Romans which dominated the church it worshipped. When the Arabs conquered the Sassanian empire in the 7th century, almost the entirety of the empire had previously been Zoroastrian was converted to Islam. This covered the Kurds too.

The Armenians in the Arab empire were able to continue their worship of Christianity. Arab rule gave relative autonomy to Armenia and many governers of the region were Armenian themselves.

In summary, the early process of distinction the Armenian kingdom had from first, its Zoroastrian neighbours (by adopting Christianity as its state religion and then resisting Persian efforts to impose Zoroastrianism), and then the Christian Church (by rejecting the Council of Chalcedon) caused it to be so uniformly Christian for so long.