A background: We have seen a lot of prominent Hindu Leaders, spiritual and Socio-political alike answering the question: that all the religions are the same. I have yet to see this answer when asked to an Islamic or a Christian Clergy.So, Are all religions the same or is just Hinduism engulfed in the myth of Sameness of all religions?
Vedanta is unique among religions as it is founded on principles, not a particular personality. Swami Vivekananda says (Complete Works, V3 pp 249-251, also available here under the heading Lectures from Colombo to Almora, sub-heading The Sages of India, http://cwsv.belurmath.org/volume_3/vol_3_frame.htm):
This is a peculiarity which we have to understand — that our religion preaches an Impersonal Personal God. It preaches any amount of impersonal laws plus any amount of personality, but the very fountain-head of our religion is in the Shrutis, the Vedas, which are perfectly impersonal; the persons all come in the Smritis and Puranas — the great Avatâras, Incarnations of God, Prophets, and so forth. And this ought also to be observed that except our religion every other religion in the world depends upon the life or lives of some personal founder or founders. Christianity is built upon the life of Jesus Christ, Mohammedanism upon Mohammed, Buddhism upon Buddha, Jainism upon the Jinas, and so on. It naturally follows that there must be in all these religions a good deal of fight about what they call the historical evidences of these great personalities. If at any time the historical evidences about the existence of these personages in ancient times become weak, the whole building of the religion tumbles down and is broken to pieces. We escaped this fate because our religion is not based upon persons but on principles. That you obey your religion is not because it came through the authority of a sage, no, not even of an Incarnation. Krishna is not the authority of the Vedas, but the Vedas are the authority of Krishna himself. His glory is that he is the greatest preacher of the Vedas that ever existed. So with the other Incarnations; so with all our sages. Our first principle is that all that is necessary for the perfection of man and for attaining unto freedom is there in the Vedas. You cannot find anything new. You cannot go beyond a perfect unity, which is the goal of all knowledge; this has been already reached there, and it is impossible to go beyond the unity. Religious knowledge became complete when Tat Twam Asi (Thou art That) was discovered, and that was in the Vedas. What remained was the guidance of people from time to time according to different times and places, according to different circumstances and environments; people had to be guided along the old, old path, and for this these great teachers came, these great sages. Nothing can bear out more clearly this position than the celebrated saying of Shri Krishna in the Gitâ: "Whenever virtue subsides and irreligion prevails, I create Myself for the protection of the good; for the destruction of all immorality I am coming from time to time." This is the idea in India.
What follows? That on the one hand, there are these eternal principles which stand upon their own foundations without depending on any reasoning even, much less on the authority of sages however great, of Incarnations however brilliant they may have been. We may remark that as this is the unique position in India, our claim is that the Vedanta only can be the universal religion, that it is already the existing universal religion in the world, because it teaches principles and not persons. No religion built upon a person can be taken up as a type by all the races of mankind. In our own country we find that there have been so many grand characters; in even a small city many persons are taken up as types by the different minds in that one city. How is it possible that one person as Mohammed or Buddha or Christ, can be taken up as the one type for the whole world, nay, that the whole of morality, ethics, spirituality, and religion can be true only from the sanction of that one person, and one person alone? Now, the Vedantic religion does not require any such personal authority. Its sanction is the eternal nature of man, its ethics are based upon the eternal spiritual solidarity of man, already existing, already attained and not to be attained. On the other hand, from the very earliest times, our sages have been feeling conscious of this fact that the vast majority of mankind require a personality. They must have a Personal God in some form or other. The very Buddha who declared against the existence of a Personal God had not died fifty years before his disciples manufactured a Personal God out of him. The Personal God is necessary, and at the same time we know that instead of and better than vain imaginations of a Personal God, which in ninety-nine cases out of a hundred are unworthy of human worship we have in this world, living and walking in our midst, living Gods, now and then. These are more worthy of worship than any imaginary God, any creation of our imagination, that is to say, any idea of God which we can form. Shri Krishna is much greater than any idea of God you or I can have. Buddha is a much higher idea, a more living and idolised idea, than the ideal you or I can conceive of in our minds; and therefore it is that they always command the worship of mankind even to the exclusion of all imaginary deities.
This our sages knew, and, therefore, left it open to all Indian people to worship such great Personages, such Incarnations. Nay, the greatest of these Incarnations goes further: "Wherever an extraordinary spiritual power is manifested by external man, know that I am there, it is from Me that that manifestation comes." That leaves the door open for the Hindu to worship the Incarnations of all the countries in the world. The Hindu can worship any sage and any saint from any country whatsoever, and as a fact we know that we go and worship many times in the churches of the Christians, and many, many times in the Mohammedan mosques, and that is good. Why not? Ours, as I have said, is the universal religion. It is inclusive enough, it is broad enough to include all the ideals. All the ideals of religion that already exist in the world can be immediately included, and we can patiently wait for all the ideals that are to come in the future to be taken in the same fashion, embraced in the infinite arms of the religion of the Vedanta.
So, yes, Vedanta is unique in that it can include all religions within its umbrella.