If you investigate freemasonry and religion, among the first things you will find are various iterations of the following message:
Freemasonry is not a religion, and is not intended to be a replacement for religion. Within the ranks of the brotherhood are many people of varying backgrounds and faiths. Lodges in one part of the world may have more members of a particular faith than those in other parts, but regardless of this, believers of all faiths are welcome. The teachings and rituals of freemasonry are intended to be acceptable to all religious traditions, and the organization encourages its members to practice their chosen faith, and to serve God above all man-made institutions.
While this is true, the relationship of freemasonry to various religions has gone through phases, and evolved over time. Some religions or sects have regarded freemasonry with suspicion, or in some cases, outright condemnation. Meanwhile, some of the rituals and symbolism used in Lodge clearly are traceable to particular religions, such as the Judeo/Christian. Does this mean that freemasonry is particularly Christian or Jewish, as opposed to any other faith? What is its compatibility with other, non-Christian faiths?
Freemasonry’s Historical Relationship with Christianity
Coming, most recently, from Europe in the first and second millennia C.E., it should not surprise us that freemasonry has been influenced by religion, specifically Christianity. While the York Rite has many Christian elements, this is only an appendant body, whose degrees are not essential to being a Mason. Beyond this, the common use of the Bible as the Volume of the Sacred Law (or Lore) in the rituals is more-or-less the extent of specifically Christian symbolism in freemasonry, and even that is not ubiquitous among lodges and orders.
On the other hand, from a historical perspective, many believe that speculative (philosophical) Freemasonry might not exist today, if not for Christianity. This is due to the fact that much of what makes freemasonry so unique and valuable is to some extent the result of Christian oppression. In this sense, religion in the form of Christianity may have shaped Freemasonry far more from the outside than from the inside, at least according to many masonic historians, such as the masonic history described by Manly P. Hall.
During what we normally call the Dark Ages, various Western wisdom traditions, tracing their origins to the mystery schools of the ancient world, found refuge in the the ranks of operative masonry, among those who were truly stonemasons by trade. The operative masons’ democratic organizational structures, political independence, and secretive nature made this guild-like organization an appealing place for those who were considered heretics under the rule of the Catholic church. Within its ranks, they could practice and carry on their traditions in safety, and freely exchange ideas, blending the ancient wisdom teachings with the more literal craft of the masonic trade.
The fusion of these refugee practitioners of gnosticism, hermeticism, alchemy, astrology, and related systems with the operative builders of old is the origin of speculative freemasonry, as we know it today, and it all happened in part because of the religious tyranny of the church. Not only did freemasonry as we now know it come into existence partly to conceal themselves from the persecution of the church, but also subverted it in some ways, such as by being heavily involved in the secret colleges which ultimately culminated in the scientific revolution, and scientific enlightenment, displacing the Catholic church as a monopoly on truth. Yet, does this mean that Freemasonry was inherently anti-catholic, or anti-christian?
Freemasonry is primarily a collection of traditions and rituals, none of which are explicitly against any religion, but in fact are supportive of religion. What Freemasons generally are opposed to are tyranny over the minds and lives of people. Freemasons have been, throughout history, proponents and defenders of personal liberty, including the freedom to think, believe, speak, and worship as each person sees fit, as well as the ideal of self-rule and democratic forms of government. In fact, many masonic historians claim that our organization was instrumental in the democratic uprisings of the 18th century, including both the French and American revolutions.
In this light, we can safely say that freemasonry’s rocky historical relationship with Catholicism had less to do with their beliefs, and more to do with their imperial and dogmatic rule, which persisted even after the fall of the Roman Empire. Since the fall of that empire, freemasonry’s relationship to Catholicism and protestant Christianity has been much more congenial, even symbiotic, with many Masons also being members of various churches and clergy.
Conservative or Fundamentalist Religions
While much of freemasonry’s historical context is in relation to Catholicism, it has of course interacted with many other religions, as well. It might be safe to say that the theme is not so much variation in freemasonry’s attitude towards the various religions, 
as we believe in freedom of individual worship, but rather in those other religions’ attitudes towards freemasonry. Often, the most conservative of these religions have a strong aversion to the theologically liberal nature of masonry.
The Muslim world is an excellent example. For various reasons, the Islamic peoples of the world have not generally had a very favorable view of Freemasonry, with it being totally banned in some Muslim countries. This seems to be due primarily to the Judeo-Christian flavor, symbolism, and historical lore of some aspects of freemasonry.
On the other hand, one appendant body of Freemasonry, the Shriners, clearly has Islamic symbolism, and some even trace their history to the first followers of Mohammed. Writers on the subject tie the Islamic opposition to freemasonry mostly to their political opposition to Judaism, and the long-standing rivalry between these two branches of the Abrahamic faiths.
Another group with a strongly antipathetic view on Freemasonry are some modern evangelical Christian sects, as well as some other protestant bodies. The details of their various stances are too great to go into, but generally they tend to associate Freemasonry with the occult, and therefore satanism, witchcraft, etc. Another common thread among both Evangelicals and Islamic people is the idea that Freemasonry is a Jewish conspiracy, mostly based on the prominent symbolism of Solomon’s Temple.
In general, those religious groups most opposed to Freemasonry are also those who are most opposed to freedom of religious thought, and those which are friendliest towards it are the most religiously liberal. Regardless of this, Freemasonry itself welcomes people of any particular faith.
Freemasonry and Non-Abrahamic Faiths
The relationship of Freemasonry to other belief systems outside the domain of 
Abrahamic religions follows the same aforementioned pattern; however, since non-Abrahamic religions tend to be less restrictive on personal freedom of thought, the relationship tends to be more often positive or neutral.
Hinduism in India, for instance, is generally accepting of all forms of worship as being within the myriad ways in which one can come to know God, Brahman or the absolute, and as such, freemasonry is usually regarded as another one of those ways, albeit one from a totally different cultural context, the West. Just as Hindus can accept Christ as a great saint, so they can usually accept freemasonry as a spiritual practice. Because of the British imperial rule, Freemasonry has had a presence there, and some believe that freemasonry has played some part in merging of East and West in India.
Likewise, there is not much in Buddhism which is opposed to masonic ideals and practices, and many masons practice some form of it. Today, some orders of freemasonry, most notably Universal Co-Masonry, are particularly friendly towards Eastern philosophy in general, even sometimes using the Vedas or I-Ching as our volumes of sacred lore. This is due in part to our historical ties to Theosophy, and consideration of the Eastern origins of much of Western esoteric tradition.
Lastly, what about Interfaith, Wiccan, Neo-shamanic, Pagan, New Age, and similar non-denominational, eclectic forms of spirituality? As with every other belief system, these should be welcome in freemasonry, so long as they believe in a singular, primary Higher Power, regardless of various sub-deities which may also be worshiped.
As far as which Order of Freemasonry this type of person might find most compatible, the main thing to consider is the culture of the brothers in the lodge; the more liberal and universal, the better. Membership in a primarily Christian or Muslim lodge may be possible, but might still feel out-of-place.
In that sense, Universal Co-Masonry, which is generally more religiously liberal as well as more mystically or spiritually oriented, is likely to be a more comfortable community for anyone on this type of path, the difference being primarily not in the rituals themselves, which are much the same as masculine masonry, but in the culture of the membership, and of course the lack of segregation by gender, race, or any other attributes.
