It depends on the nature of their non-acceptance.
If they accepted Islamic rulership, but did not convert to the religion of Islam, they were called Ahl ad-Dhimma, meaning "Protected People". A subset of the Ahl ad-Dhimma were also called Ahl al-Kitaab, meaning "People of the Book" and usually used in reference to Jews and Christians.
If they did not accept Islamic rulership or the religion of Islam, they were called "Unbelievers" or "Infidels". The Arabic term used was typically, Kuffar, meaning "those who deny the Truth about God".