The act of reconstructing is itself absolutely a process or methodology. I've never seen anywhere that has been disputed. However, that being said, to view Celtic *Reconstructionism* as a spiritual practice, religion, or way of life is not some wild idea born from a couple of people misunderstanding of The CR FAQ. I honestly haven't the foggiest idea as to why "CR as a spiritual practice" seems to ruffle feathers as we are not contradicting anything. In fact, I feel the FAQ is quite clear on it being both:
"Most of us are very spiritual people in our private lives. We have altars in our homes and do personal and family-centered devotional work. Some of us do divination or healing, or perform ritual services within our communities. Reading doesn't mean we're not spiritual. In fact, for most of us, the reading we do enhances our spirituality and helps us understand what we are taught by other people and what comes to us through more mystical means such as in visions, meditations or dreams. Reference books, written by those who have devoted their lives to studying the words and traditions of the ancestors, help us sort out what is traditionally Celtic from what is our own internal voice. Both may be valid, but our inner voice may not be entirely accurate about what is Celtic, or what is communication from the Divine and what is our own imaginations. When we believe we are receiving information from a Deity or spirit, we go to the scholars to compare notes and see what's Celtic and what's not.
The CR community is diverse. Not everyone is an experienced scholar, and not everyone is inclined to deep mystical work. However, we believe both scholarship and experiential, ecstatic spirituality are necessary on the CR path. The presence of, and balance between, these aspects is crucial. Without both, it is not CR. But people will tend to move towards what is more comfortable and desirable for them. Sometimes the balance has to be found in community, where the mystics and the scholars can work together to help inform one another's practices. In this way, we can co-create a vibrant tradition that honors our personal experiences as well as those of our ancestors, that is ecstatic yet also rooted in the earth and in the history and living culture of the Celtic peoples." (source; emphasis mine)
So, the act (or methodology if that term floats your boat a wee bit more) of reconstructing is employed "to create a modern spiritual practice that retains as much authentic older material as possible while also being workable in the modern world," (source) and that spiritual practice is therefore the -ism portion of "Celtic Reconstructionism." The scholarship is the methodology of reconstructionism, the implementation of what is reconstructed through scholarship is the spirituality: CR is made up of both.
Further still: "along with the work of scholarship, we also rely on our own iomas and aisling—our inspiration and our visionary practices—to help us find ways to integrate old practices into a new time and setting." (source) So, technically, stating that CR was created solely, from the very beginning, as simply a methodology is incorrect; the FAQ itself disproves it. All the quotes I have shared clearly show scholarship (i.e., methodology) and spirituality as linked within Celtic Reconstructionism.
Personally, I will always see CR as a mixture of both. You need the scholarship of reconstruction to create/re-build the spirituality; you can't have one with the other, imho. But I do feel we are actually moving away from needing to employ the so much of the methodology side straight from the get-go as much as we have in the past; as a lot of the work has already been done.* New people no longer need to first go through the act of reconstruction in order to begin a practice. Places like Tairis have put the information and research out there, free of charge; it simply needs to be implemented in spiritual practice, in the -ism.
* I'm, of course, not saying everything has been reconstructed, there's still a lot to be tackled. But the foundations for basic practice pretty much have been covered; at least for those focusing on Gaelic traditions. I can't speak for how much work has been done in reconstructing other Celtic traditions as I'm not a part of them.