If you mean a "uniform religion" - as in everyone believing, professing, worshipping, dressing and speaking with the same words - then a resounding "no!". I think that would be the closest thing I can imagine to a true dystopia, especially if the said religion were hierarchical. It would probably be worse than George Orwell's 1984 or the Hunger Games....
There is a line of thought, exhibited by many sociologists and even spiritual leaders such as his Holiness the Dalai Lama which posits that human beings are far too diverse in temperament, taste, mindset, attributes and intimations to ever conceivably become united under one common faith or religion.
I concur with this. It just isn't human nature as I see it.
However I suppose it depends upon what form of religious unity one is proposing. Certainly, their will never be uniformity. History has taught us that where a society has attempted to impose identical, uniform customs, rituals, religious/ideological laws, linguistic expressions, forms of worship, styles etc. on vast congregations of people from different nations and cultures it has inevitably failed, since true unity can only exist in and through diversity.
There is a different understanding of religious unity, however, which I think could be possible.
This is the kind of unity where there exists a plurality of rites each with their own distinctive theologies, liturgy, art, literature, rituals, customs, traditions, ceremonies, prayers, styles of prayer, terminologies that while not uniform are nevertheless only different expressions of some common fundamental truths.
Each of these religious rites are truly self-governing - they retain their distinct sense of self-identity, autonomy and governance while also pledging complete loyalty to the higher, universal ideal or "meta-belief" which governs the whole.
While I wouldn't consider this to be "desirable"
per se, I could envision it as at least functioning.
A cardinal of the Catholic Church called Nicholas of Cusa, offered up this vision in the 1400s:
"...With many groanings I beseeched the Creator of all, because of His kindness, to restrain the persecution that was raging more fiercely than usual on account of the difference of rite between the religions...We praise our God, whose mercy rules over all His works and who alone has the power to bring it about, that such a great diversity of religions would be brought together in one harmonious peace. We, who are His work, cannot disobey His direction. Nevertheless we request instruction, as to how this unity of religion can be introduced by us...You will find that not another faith but the one and the same faith is presupposed everywhere...There can only be one wisdom. For if it were possible that there be several wisdoms, then these would have to be from one. Namely, unity is prior to all plurality...Even though you acknowledge diverse religions, you all presuppose in all of this diversity the one, which you call wisdom...Therefore, come to our aid you who alone are able. For this rivalry [among religions] exists for sake of you, whom alone they revere in everything that all seem to worship. For each one desires in all that he seems to desire only the good which you are; no one is seeking with all his intellectual searching for anything else than the truth which you are. For what does the living seek except to live? What does the existing seek except to exist? Therefore, it is you, O God, the giver of life and being, who is being sought in different religions in different ways, and who are named with different names because as you are you remain unknown and ineffable to all...Therefore, do not hide Yourself any longer, O Lord. Be propitious, and manifest Your face; and all peoples will be saved, who no longer will be able to desert the Source of life and its sweetness, once having foretasted even a little thereof. For no one departs from You except because He is ignorant of You...Moses had described a path to God, but this path was neither taken up by everyone nor was it understood by everyone. Jesus illuminated and perfected this path; nevertheless, many even now remain unbelievers. Muhammad tried to make the same path easier, so that it might be accepted by all, even idolaters. These are the most famous of the said paths to God, although many others were presented by the wise and the prophets...Even though you acknowledge diverse religions, you all presuppose in all of this diversity the one...It is you, O God, who is being sought in various religions in various ways, and named with various names. For you remain as you are, to all incomprehensible and inexpressible. When you will graciously grant it, then sword, jealous hatred and evil will cease and all will come to know that there is but one religion in the variety of religious rites..."
- Cardinal Nicholas of Cusa (1401 –1464), De Pace Fidei, Catholic mystic and highest cleric under the Pope in his day
una religio in varietate rituum = one religion in a variety/diversity of rites/faiths
In response to the fall of Constantinople in 1453, Nicholas of Cusa wrote De pace fidei defending a commitment to religious tolerance on the basis of the notion that all diverse rites are but manifestations of one true religion
Nicholas of Cusa