I would define a (metaphorical) priesthood as an organization accepted as an unquestionable authority on a realm of questions ("mysteries"), whose membership is self-regulated, and that access to the "mysteries" is to be gated exclusively by fully initiated members of the organization. Worship of the "mysteries" is encouraged by the priesthood to enhance the priesthood's authority.
I am not sure it was being used in the sense of "worship," but rather by the notion of there being certain elites who get to control what is considered to be orthodox, what is heterodox, and what is so heterodox that it shall not even receive a hearing (usually for the good reason that it's obviously wrong, but surely not always).
It is a fair question as to why string theory received serious discussion and so much study by trained scientists, whereas other theories are dismissed without a full hearing, The technical reason is just that string theory arose in a context where multiple people were pondering similar unanswered questions, and it was able to grow organically among people who were part of the established (forgive me) priesthood, whereas most other theories derive from people who are not established in scientific circles. Add to that, that giving a full hearing to every crackpot theory would have a substantial cost in time and manpower that could be more efficiently spent. That said, if string theory ultimately proves to be incorrect, oh my heavens! Future generations will quite rightly mock us over the waste of time in which we are presently engaged!
(How did the early 21st-century scientist die while raking leaves? He fell out of the tree.)
(An early 21st-century scientist and his buddy are at a bar after work. A video comes on the TV of a woman standing on the ledge of a building. The scientist says, "I'll bet you $10 she doesn't jump." The buddy takes the bet and the woman jumps to her death. When the scientist hands over the $10, his buddy says, "No, I can't take it. Truth is, I saw that story on TV earlier when I went home to eat lunch." And the scientist says, "I saw it earlier too, but I never thought she'd jump a second time!")
That said, I have not read the book, so perhaps the term was being used in an unfair way, but from the context I am not certain that it is. I doubt she means to say "Science is a matter of belief." I think Shermer would take her to task if that were the point.