While I'm a Christian who has little in common with Freemasonry and the Shrine, I have problems with such harshness. I think that most of what the outside thinks about the origins of their symbols comes from antipathy rather than understanding. Instead, I'm inclined to believe their own reports about their origins and symbols, even if I disagree with what these things represent.
As you can read in the Shriner Primer, the first reference below, the Shrine claims to have started because the regular Masons were too stuffy and business-like and these boys wanted to have some fun. So following a NY party thrown by an Arabian diplomat, Walter M. Fleming, M.D. and actor Billy Florence (both Masons) came up with the idea of a fraternity that would allow like-minded Masons their fun and hijinks. Aside from the reception, there was a general interest in things Middle Eastern back in the later 1800s and their organization reflects that.
Their official name, The Imperial Council of the Ancient Arabic Order of the Nobles of the Mystic Shrine, is actually highfalutin hogwash. "Council" is the most accurate term in the list. They aren't imperial (most are everyday Joes), ancient (begun in 1870 and first officially meeting in 1872), Arabic (except by copying certain externals), or noble (at least regarding actual royalty). I'm not even sure about the "order"; the group is organized and governed by its own rules but their conventions have a disorderly reputation of almost epic proportions.
Finally, the "Mystic Shrine" has no geographic counterpart. It is mystic in that it only exists within the minds of Shriners. I suppose that the phrase was chosen because it sounded good, because it hearkened to the secrecy of standard Masonic rituals, and because it hints of a quasi religious status.
As for the fez, this Moroccan headgear was popularized as part of the period's general enthusiasm for the Middle East I noted above. This attitude shows itself in much of that time's literature, including Mark Twain's classic, Innocents Abroad (see below).
As I also stated, I have little use for Masonry and the Shrine, but my reasons are related to my faith in Christ and the espoused beliefs of these organizations, not by myths originated by outsiders. You can see some of what I mean in the final reference I provide.