Nothing makes them more "worthy" of empathy. It's that I have somewhat more of a personal connection to them. During my studies the Arab Christians on the campus in Tel Aviv were some of the most peaceful and kind people I met over there and it influenced me greatly.
They also happen to be caught between a rock and a hard place where both the Israelis and the Muslim Palestinians both oppress them. Quoting from [1]:
I am a Christian by religion, born in Nazareth, Israel to
Arabic-speaking Christian parents and brought up in Kufur Yasief,
the hiding place of Josephus Flavius
Persecution for Christians in Israel and Palestine is not on the
scale it is in Egypt, but it is there nonetheless. It must be added
that there is a growing number of Jewish-background, and Russian
Christians in Israel, who suffer more persecution from the
Jewish state and people.
...
Christian Arabs in Israel/Palestine live in a climate of fear
and therefore hypocrisy. Pressure on Arabic-speaking Christians
to tow the Muslim Arab nationalist line is so great, that we are even
afraid of complaining about injustices against us.
We suffer:
• At the hands of Jews, because we are seen as:
o Arabs: and so enemies, and primitive.
o Christian: and so gentiles. WE are often blamed, by association,
for the European holocaust.
• At the hands of Muslims because we are Christian, and "infidels."
We are often punished for “western” bias towards Israel.