agreed that "transfer" sounds and feels similar to "transplant". But imo the "transplant" part in "fecal matter transplant" was not the part that was problematic for public perception lol.

I think both "digestive microbiome transfer" and "digestive microbiome transplant" sound perfectly fine, as both get rid of the "gross" part of the name. But I think that "transfer" is slightly better, because "transplant" invokes associations with something being surgically put into my body and attached to stay there permanently. While "transfer" doesn't have the same sense of permanence and seriousness attached to it.