This is going off the Wiki article, with no other knowledge of Melungeon people.
While there may not be any evidence located to define 'why' they were referred to as portugese, we can propose a few theories.
2)Lack of another more accurate word for the colonials to use. The terms 'Native American, and African American' would not come into existence until many years AFTER America became a country.
3)Due to needing to come up with a term to call a mixed people may have led to the use of 'Portugese' as a side or private joke, which then went into general use.
4)A slur. If Portugese people were seen as a substandard mix to colonials and the word was used as a slur, (such as in speaking negatively about the Moor-Iberian mixed people of Portugal) they could have transferred it to this mixed people in the new world.
5)A Portugese person or person(s) settling in that area, perhaps a sailor from an incoming ship (from any country), that contributed to the mix of that pocket of people.
One big reason was the claim by melungeons themselves that they were 'portuguese' as a way to escape stigma and discrimination for their African heritage. I'm from appalachia myself and know some people who are melungeon and it was a conscious and safe survival strategy during the days of jim crow to try and hide your black ancestry...