Greetings of Peace. I generally avoid the designations traditionalist and perennialist because they create the false impression of an ideology, but I understand your question so I will not belabor the point. As Schuon is widely considered one of the central figures of the traditional school, an appeal to his teachings is pertinent in illustrating the general view of this topic. He has two primary considerations that you can read about in detail in the first and third chapters of Gnosis: Divine Wisdom. The first is as follows:
"Religions are separated from each other by barriers of mutual incomprehension, and one of the principal reasons for this seems to be that the sense of the absolute is situated in each case on a different plane, so that points of comparison often prove illusory. Elements resembling one another in form appear in such diverse contexts that their function changes from one case to another, and as a result their nature changes as well ..."
Examples of the sense of the absolute situated on different planes can be seen within the categories of The Paths to the Summit section of our forum and their supporting quotations. Suffice to say that unless a person has a propensity for understanding metaphysical doctrines, it is not possible to reconcile these perspectives except in an inadequate and ultimately illusory manner. An often overlooked point that is emphasized by both Guenon and Schuon is that the goal of religion is not to communicate such doctrines, but rather to save souls, essentially by establishing a divinely ordained system of beliefs, worship, and ethics. Metaphysical doctrine, including its corollaries such as the transcendent unity of religions, is quite exceptional in this context as most people do not have a propensity for it. Nevertheless, the challenges to religion proposed by modernism and secularism necessitate a recourse to metaphysics in order to preserve and defend the integrity of the faithful. This is in essence the public program of the traditional school carried out through its various writings.
To return to Schuon's second point, he also wrote that, "If Revelations more or less exclude one another, this is so of necessity since God, when He speaks, expresses Himself in an absolute mode; but this absoluteness concerns the universal content rather than the form, to which it applies only in a relative and symbolical sense, for the form is a symbol of the content and so too of humanity as a whole, to which precisely this content is addressed. It cannot be that God would compare the diverse Revelations from the outside as might a scholar; He keeps Himself as it were at the center of each Revelation as if it were the only one. Revelation speaks an absolute language because God is absolute, not because the form is absolute; in other words the absoluteness of the Revelation is absolute in itself, but relative in its form."
This is basically saying that each revelation is uniquely a manifestation of the absolute, the quality of which is reflected in its totality and comprehensiveness. Each tradition is a self-contained locus of the manifestation of the Divine which does not require any other revelation to complete or explain it. Concerning the denominations, these are a reflection of God's Infinitude, and constitute so many actualizations of the possibilities inherent in a Revelation. From the perspective of their adherents, each exalts the denomination itself to the status of the tradition as a whole and sees within it the absoluteness of the Revelation. One may easily find fault with this perspective from a metaphysical point of view, but it does not necessarily preclude genuine participation in the Revelation ...
One of the functions of this type of criticism is to demarcate boundaries that establish a unique identity for one's position. The Brahma Sutras proposed to reconcile the teachings of the Upanishads and Bhagavad Gita and establish an indentity for the Vedanta perspective by separating it from other prevalent perspectives. The latter task it accomplished through the foundational subject of causality, proposing that Brahman is the sufficient cause of all things. In the second chapter, it focuses solely on this subject in its criticism of the different schools, but does not propose a systematic refutation of the various perspectives as a whole. One may even go so far as to say that the diversity of the perspectives considered may indirectly testify to the universality of the Vedanta or at least of the author, but this is not the generally accepted view.
Guenon identifies what are now popularly considered to be the six darshanas or orthodox points of view. He actually references the above chapter of the Brahma Sutras and is careful to demonstrate the manner in which each of these darshanas is reconciled within the metaphysical outlook of the Vedanta. A useful way to understand the intricacies of Guenon's perspective concerning the different points of view emerging from a single underlying body of doctrine, is to consider the difference between the teachings of Plato and Aristotle and the manner in which they were both accepted to integrated into the philosophy of the post-Plotinian Platonic Philosophers. Although, like the author of the Brahma Sutras, Aristotle was critical of Plato on certain points , the later philosophers viewed them both as explicating a single doctrine albeit through different methods and starting points. Aristotle proceeded inductively from the analysis of the many and Plato proceeded deductively from the contemplation of the One. A direct parallel can be seen within the comparison of Sankhya and Vaisheshika. Guenon writes that "Universal manifestation can be looked at in two different ways; either synthetically, starting from the principles out of which it proceeds and which determine it in its every mode - this is the point of view of Sankhya ... or else analytically, in the distinguishing of its manifold constituent elements, and this is the line of approach of Vaisheshika."
Guenon's acknowledgement of the authenticity of different perspectives of the Hindu Doctrine is also shared by Sri Chandrasekharendra Saraswathi, the revered 68th Jagadguru of Kanchi, as evidenced by his writing Many Paths to the Same Goal.
Greetings of Peace. This blog contains selections from my correspondence and other sources on a variety of subjects related to religion, philosophy, and spirituality. I hope that they may be of benefit to the interested reader. Concerning the title of the blog, read this entry.