I think there's a difference between "people of the book" (Jews & Christians) and "dhimmis" (non-muslims under Islamic rule) the latter have less freedom.
and the thing is, neither christians OR Jews consider
muslims to be people of the book.
Depends on what type of Christian you talk to. A right-winger from Europe or N. America will probably say muslims worship the devil. A Palestinian Christian will probably reply in a totally different way. The brotherhood amongst Arabs regardless of their faith is quite common, I know a Palestinian kid who has Islamist leanings yet refers to Arab Christians as "brothers".
Also the same can be said about muslims, most wouldn't refer to Christians & Jews as "people of the book" today because they're quite different from the Christians & Jews of the 7th century. E.g. Islamically speaking you can eat kosher meat however most muslims won't today because they say Jews aren't as monotheistic as they once were (rejection of OT laws, secularism/democracy etc)