If one cannot be Christian and Muslim, then one cannot be Christian and Arab! This is especially true as Egyptians are Copts who have been Arabised, just as Palestinians, Jordanians, Lebanese, Syrians and Iraqis are Assyrians who have been Arabised.
However, if we were to take Jewishness and Muslimness are races, then yes, we have Jewish Christians (ie those people who are racially/ethnically Jewish) and Muslim Christians (ie those people who are racially/ethnically Muslims/Arabs).
A Muslim Christian has to believe Jesus Christ is Lord and God and virgin Mary is theotokos (Mother of God). A Muslim Christian has to confess the Nicene Creed and believe in all ecumenical councills, from the Nicea right up to Vatican II. All Muslim Christians have to reject Sharia and declare Muhammad to be a false prophet.
The CCC says Muslims and Christians worship the same God, which can be interpreted as being truly Muslim means believing God is Trinity. So, vast majority of Islamists such as Hamas, Hezbollah, Shias, Sunnis, Ahmadis, Druse and Bahais are not really Muslims as they follow Muhammad’s concept of God.
The Arabic word “Muslim” just means SUBMITTER and so any Christian who submits to the Holy Trinity is a Muslim.