There are different definitions of syncretism. Generally I think syncretism best describes the practices of religions or cultures that have over time interacted with other religions and cultures and thus to some degree blended practices and or beliefs from more than one spiritual system. To some degree all major world religions are syncretic. Some religions are more syncretic than others. Sometimes it is a particular culture or group within a religion that is syncretic and possibly at odds with the presumably orthodox, official version of the religion.
In the case of this thread syncretism seems to be referring to what I call eclecticism, and individual who blends elements of more than one religion into a personal system.
Whether a particular practice qualifies as syncretic is simply going to depend on definitions. I do not overtly mix elements of different religions systems: often this runs into issues of cultural misappropriation, not to mention poorly thought out thinking and ritual, although there are exceptions. Eclecticism/personal syncretism can certainly be done in a well thought out and ethical manner.
While I do not overtly mix elements of different religions my own rituals draw from ideas that are influenced by other religions such as Buddhism. Some elements are influenced by mysticism (of the I-am-God variety) which in turn may have influences traced back to sources we usually identify as Gnostic. Pantheistic, monotheistic, and polytheistic elements are present and depending on how one wants to focus on different elements of the liturgies one could take different interpretations or approaches. Some elements are based in personal experience. One prayer in particular is obviously influenced by the Law of Thelema. Mostly my rituals consist of prayers from the traditional Book of Common Prayer and Anglo-Catholic sources, re-structured and patterned around core prayers of my own devising, thus conveying a very different theological picture. Yet it would be very familiar to Anglicans accustomed to the traditional liturgies. The whole framework is strongly suggestive of postmodernism. The whole thing could be considered syncretic on a personal scale or in other words eclectic.
Why do this? Because there are so many problems with traditional Christian doctrine. It is based on incredible myths mixed with elements of history. That is fine by me except that I am expected to swallow it as fact-based according to most traditional doctrine, and I find that unfathomable. Of course my particular branch of Christianity is lenient in terms of my personal beliefs. But that does not solve the whole problem. Christianity has a deeply anti-Semitic history. I have had to re-structure the Divine Office and am continuing to find a way to integrate it into my personal eclectic practices because of the way its lectionary and other elements portray our parent religion so often.
Liberal elements of the Church of course are more sensitive to these issues, but they lose on matters that traditionalist members of the church are still generally pretty solid on. Some liberal parishes for instance have devolved into self-help or social justice groups with very little of spirituality. It becomes bland, at worst a way to feel good about one's self. Which is fine! But I am looking for something deeper than that. And have you seen some of these liberal liturgies? Often they are ugly and awful. To enter into a meditative mindset via ritual I need a certain amount of order and beauty. I am not looking for the priest dressed up as a clown, or Barnie on All Soul's Day (yes, these things happen.) Secular music is great in its own context, but the Church has a long history of beautiful music. No to a jazz vespers. A 12 step addiction themed mass? Just...no.
When liberal elements of the church do not coincide with absolutely ridiculous theatrics that I could never participate in there is often an emphasis on rationality which is something very important to my own spirituality, actually, and something I value in the liberal camp, but on its own that is not complete for me.
(Edit: I should add here that while liberal Christianity had a focus on rationality this is much less true of some factions identifying as liberal in the Church today: there is a strong anti-intellectual streak and often a delving into psuedo-spiritual non-sense New Age beliefs and practices, and a tendency to want to throw away all traditional elements of prayer and liturgy uncritically. Often those elements have been misunderstood and mischaracterized. Often anything from the past is viewed as worthless. While I am critical of much of what has been handed down to us from Christianity's past including some elements of the liturgy and the impact it has had on the Jewish people among others this side of things often gets little attention among such people and such elements are still present in most modern liturgies without most laity taking notice at all including the liberal camp. I believe many important and beautiful elements of liturgy, art, and architecture are being destroyed often without addressing real problems.)
Basically my practices are a protest against certain elements in the Church both traditional and liberal. It is also a commentary on the doctrine and an alternative vision, a different theological take, and an approach influenced by postmodernism among other sources.
Why not join another religion? There are a few reasons. I am not sure that I would be any less critical of another religion than I am of my own Christianity, actually. And there would be a major downside: since I am not culturally familiar with those religions I would be in less of a position to critique them. It is also true that I simply do not resonate with other religions the way I do with the one I am culturally familiar with. The psalms, the Rosary -- these sink me into a calm state in a way that I suspect Buddhist mantras never can and will. And when those familiar prayers are incorporated into my own rituals they are all the more powerful in the new meanings they can take on in that different context.
My practices grew out of personal struggles and trauma and other personal experiences that were difficult for me to process and give any language or order to. When they first emerged in their embryonic form they were a desperate attempt to give order and meaning to what was happening inside me, and to offer up my suffering. Over the years those basic rites while retaining their core have evolved because I am still not done healing. And as they evolve they take on new insights, and I move from working on my personal struggles to relating them to a grander scale, how the microcosm relates to the macrocosm. And this part is still working itself out.
Somehow I am growing through these practices and giving order to my thoughts, my emotions, and my world, the cosmos. It all started with instinctive acts of reaching out to God within myself. I value my Anglican background. It is still a part of my life. I do not think I could do what I am doing without the impact Anglicanism has had on my intellectual life, my emotions, or the liturgical formation it has nurtured me with. But what I am doing and creating on the personal level is something that no organized religion can do for me. It is something that I need to do, and there is nothing wrong with it.
If I was in a situation in which I could not attend any parish for some reason I could make it with the rites that I have created and even stay in sync with the liturgical year and Christian mysteries. This could conceivably happen for a number of reasons. But as long as that does not happen I still participate in my local parish, practicing the Anglican customs side by side with my own -- the two are very much related, the latter drawing from and re-interpreting the former. There is still something grounding and good for my psyche about having a community and to share in common rituals.