Trump’s mother was a US citizen before he was born, and in those days, you had to renounce your previous citizenship when you became a US Citizen. It is highly doubtful Trump could claim citizenship in Scotland.
Of course he could have.
Ethnic based citizenship does not care if one has become a citizen of another country.
Nor do Americans have to renounce other citizenships and never have had to be US citizens.
Many US citizens today hold two passports.
Recently there was one guy who even went back and became president of some Eastern European country. The US had no problem with that. And the European country had no problem with him being an American.