Is this rhetoric or do you actually believe this?

Islamic architecture is sublime.The Muslim prohibition of idolatry required Mughal artisans to become masters of symmetry and tesselation, giving their structures a mathematical beauty.

Are you really drawing a causal connection between the prohibition of idolatry (I'm assuming that you are referring to the Hadith that allegedly prohibit artists from representing nature) and mastering symmetry? I wonder how it is, then, that Brunelleschi was able to create the magnificent proportions of the Old Sacristy of San Lorenzo while also retaining the sculptural ability to finish runner-up to Ghiberti in the famous Baptistery doors battle. Or how Palladio was able to create the Villa Rotunda in Venice at the same time that Titian was operating. Or how Sinan was able to design all of his mosques while Ottoman miniature painting flourished. Or how the Taj Mahal's anonymous architect was able to master symmetry, while Shah Jahan simultaneously kept his court artists busy making god knows how many representations of himself.

Also, if you're going to use a word like sublime, you should understand that it has a very particular meaning in art and architectural criticism that has little to do with qualities like symmetry and tesselation.

The Taj Mahal stands as the most perfect edifice in an India

Even if we accept that the Taj Mahal is the most perfect edifice in India, as opposed to, say the Jain Temple at Ranakpur or Le Corbusier's Millowner's Association Building, it is not at all clear to me that this can be attributed to the fact that it is an exclusively Muslim building. If anything, what has long been remarkable about the Taj, and Shah Jahani architecture in general, is its Cosmopolitan nature, the way that it drew from a number of sources and traditions that Shah Jahan had brought to his court. His name, after all, is King of the World, not King of Islam. I would refer you to the work of Ebba Koch for more details.

That Aleppo was a religiously mixed city is not the point.

But it is precisely the point, just as it is precisely the point at Shah Jahan's court. You want to ascribe the qualities you love in the buildings you love to some exclusive Islamic provenance, just as Atta did. The fact is that most great Islamic architecture, indeed most great architecture, comes about from an architect's ability to distill a variety of competing ideas and influences to achieve a new synthesis. If what Atta loves about Aleppo did not occur because of some sort of experiment of Islamic isolationism, but was rooted in Islam's confrontation with other cultural ideas, then Atta's worldview is simply wrong.

Indeed, it is interesting is that the qualities you love as "Islamic" in the monumental works you cite are anathema to the qualities of the everyday architecture of Aleppo that Atta was praising. If clear and simple symmetry really were some sort of exclusively Islamic quality, shouldn't Atta embrace the symmetrical and monotnously planned "Western" portions of Aleppo?

The problem isn't that Atta viewed the world through an "architectural lens," the problem is he viewed it through an ideologically hardened lens that led him to misinterpret what he saw. Cultures for him were not porous and in flux, they were fixed, unchanging, and unyielding. I'd say, judging from your post, you suffer from the same problem. And I think that's the real path to radicalism and violence.