Believer’s Theory - what did it mean for non-Muslims to accept Mohammed?

Fred Donner holds the view that early Islam was rather inclusive, with Christians and Jews falling under this category.

The Quran, though containing verses which seem to preach pluralism, also contains verses which preach exclusivity (I.e. believers must obey the messenger, and no religion other than Islam will be accepted on judgement day) and contains many verses condemning the beliefs of the Christians and Jews (Christians worship a trinity, deify Jesus, Jews worship Ezra, etc).

It seems that to be considered a believer, adherents must have accepted Mohammed’s message. Yet at the same time, Donner’s theory proposes that Christians and Jews fell under the umbrella of Islam.

How can these views be reconciled? Could Christians continue to celebrate Christmas, drink alcohol, and pray in Churches while being considered as under the umbrella of Islam? Could Jews continue to adhere to their strict dietary restrictions and maintain their prayer practices and be considered under the umbrella of Islam?

What does it mean that Christians and Jews could remain so while falling under the umbrella of Islam, being that they had to accept Mohammed’s message?