The priest / king of Salem was:
1) Not a Jew -- he pre-dated the covenant with Abraham, let alone Moses.
2) Since the levitical priesthood was AFTER the King of Salem and G-d told Aaron his was the only priesthood after Sinai and that it was an ETERNAL priesthood what does it matter what came before Aaron???
Yep it is not possible for a priest from Levi to be a King or a King to be a Levi.
But since they need to somehow explain that a priest made the sacrifice they grasp at the Melchitzedek straw.
Melchi-tzedek as your Xian also stated (but seemed to ignore) was not a Jew let alone a Jewish priest, ergo he could not bring a Jewish sacrifice.
Xians like to say "Abraham brought tithes to Melchitzedek." They think this because that is what the GT says. The GT gets it wrong (as it gets so much wrong). It was ABRAM, not Abraham who brought tithes to the King of Salem.
This is important bcause Abram did not yet have a covenant with HaShem.
But who IS the King of Salem? The Xians say he was some mythical being without parentage. Nonsense. Salem is Jerusalem and the King of Jerusalem (Salem) in those days was Shem, the son of Noah.
He was a g-g-g-gandfather to Abram BTW. Which also means he was a g-g-g-g-g-g(etc) grandfather to Aaron and the Levitical priests (as well as all the other tribes).
I wish Xians could get the concept of chronology!!
BTW, Melchitzedek is not a name, it is a description: righteous (tzedek) king (melchi). So all Genesis is saying is that the King of Salem was a righteous king.
The Xians further confuse things by misreading Psalm 110 where King David is called a righteous king (melchitzedek).
Tell your Xian friend to read the Tanach where it says repeatedly that ONLY the Levites, descendents of Aaron can be Jewish priests. It is an ETERNAL priesthood. These are the little details Xians tend to ignore.
]• “And they shall have the Priesthood as a statute forever, and you shall consecrate Aaron and his sons.” (Ex. 29:9)
• “Bring close Aaron your brother and his sons with him from among the children of Israel to become Priests to Me [for all time].” (Exodus 28:1)
• “And anoint them as you anointed their father, that they may serve Me, and it shall be for them an appointment to an everlasting Priesthood throughout their generations.” (Exodus 40:15)
• “You and your sons with you shall keep your Priesthood. I give your Kehuna/Priesthood as a gift of service.” (Numbers 18:7)
• “It is an everlasting covenant of salt before G-d with you and with your descendants.” (Numbers 18:19)
• “And it shall be to him and to his descendants after him a covenant of everlasting Kehuna/Priesthood.” (Numbers 25:13)
• “For G-d your G-d has chosen him of all your tribes to stand and serve with the name of G-d he and his sons forever.” (Deuteronomy 18:5)