good luck

The term "orthodox" in English means the conformist, traditional way that does not allow for new ideas and holds old beliefs very dear. You can also use the Arabic term "أرثودكسي" but this then kind of limits you to the Eastern Churches (Greek, Coptic, Syriac, etc.) and does not necessarily convey the meaning you have in this context.

The piece you are translating is not easy to translate because it is poorly written. For one thing, it uses the present tense when the reference is actually to the past. And if that is not confusing enough, the sentence that refers to "orthodox theology" is lost in space: there is no way to tell what it is referring to. It is not clear whether the "decline of this cultural and scientific flowering" that it bemoans is the decline in Arab-Islamic culture or in European culture. The answer may very well be in another part of the text.

On the one hand, the sentence refers to a "decline of THIS cultural and scientific flowering..." What does the word THIS refer to? Are we talking about the decline that followed THIS flowering in Islamic lands?

On the other hand, the piece talks about an adverse attitude towards Aristotle, which was more characteristic of European culture up until the rise of Thomism. So is THIS decline a European phenomenon?

Despite this confusion, one thing is definite: The word "orthodox" has nothing to do with the Orthodox Church. The name of the Church is always capitalized. As bad as this writer seems to be, he/she seems to be careful about capitalization. "Avicenna," "Averroes," "Europe," and "Aristotle" are all properly capitalized. So the reference is to general religious orthodoxy, not a particular denomination or sect.

If the reference is to a supposed rise of orthodoxy in Islamic lands, then you can refer to that as

رُجحان كفة السلفية
تعاظُم سلطان أهل السلَف

In other words, "orthodox theology" would refer to العقيدة السلفية, as opposed to the fancier theologies of the sufis, the extreme forms of shi`ism, and the Hellenizing tendencies of the philosophers. Notice that I would not necessarily use the expression سـنة, for fear of confusing the issue with the Sunna as a sect. The context here is more about orthodoxy as strict adherence to doctrine than about a particular sect.

On the other hand, if the reference is to theologians in Christendom, then you can translate "orthodox theology" as Sam Berner has suggested: اللاهوت التقليدي

As Sam has pointed out, and as I explained above, nothing in the text supports interpreting the phrase as a reference to a particular Church or denomination.

Notice that Muslims do not use the term لاهوت in reference to the religious disciplines. Instead, they refer to علم التوحيد and الإلهيات

ومع تعاظم سلطان رجال الدين أو رجال الكنيسة