Once a microbiome dysfunction happens, it can evolved into more symptoms as the bacteria shifts more. Some of these evolutions may put someone out of the CFS diagnosis into a different medical diagnosis. Some of these diagnosis can be worst than CFS, i.e. Crohn’s disease.
A reader in Europe indicated several CFS/Celaic people in their group, so I will look at Celiac disease in this post.
“Celiac disease (CD) is a frequent chronic inflammatory enteropathy caused by gluten in genetically predisposed individuals that carry disease susceptibility genes (HLA-DQ2/8).” 
At first browsing of PubMed, we see close associations just like “depression and CFS” has.
- The Overlap between Irritable Bowel Syndrome and Non-Celiac Gluten Sensitivity: A Clinical Dilemma. ” Some patients with celiac disease may remain asymptomatic or have only mild gastrointestinal symptoms and thus may qualify for the diagnosis of IBS in the general clinical practice… While the treatment of NCGS is exclusion of gluten from the diet, some, but not all, of the patients with IBS also improve on a gluten-free diet. “
- Chronic fatigue syndrome and non-celiac gluten sensitivity. Association or cause?  “From my point of view fibromyalgia and chronic fatigue (FM/CFS) are not defined diseases but just syndromic terms that reflect reality… The following case, treated during the preparation of this manuscript, illustrates this relationship: a 23 year old woman with 3 years since the onset of FM/CFS with severe fatigue … After one year of follow-up, after starting diet without gluten or dairy, she presented complete remission of all her symptoms, with a normal life, practicing sports and without medication. She chose not to eat triggering foodstuffs.”
- Celiac symptoms in patients with fibromyalgia: a cross-sectional study. A list of typical celiac-type symptoms was developed, comparing the frequency of presentation of these symptoms between patients with fibromyalgia (N = 178) and healthy subjects (N = 131), in addition to those of celiac patients and gluten-sensitive patients reported in the literature. The frequency of presentation of every celiac-type symptom, excepting anemia, was significantly higher among patients with fibromyalgia compared to controls (p < 0.0001).”
- Fibromyalgia and chronic fatigue syndrome caused by non-celiac gluten sensitivity.  “The symptomatological similarity of both pathologies, especially gastrointestinal symptoms, suggests that at least a subgroup of patients with fibromyalgia could experience subclinical celiacdisease or nonceliac gluten intolerance.”
- Fatigue in adult coeliac disease.  “In coeliacs, fatigue is a common finding, which ameliorates with the gluten-free diet and is strictly correlated to depression although coeliacs on a gluten-free diet showed more frequent and more severe depression symptoms than coeliacs on a normal diet.”
What do we know about changes in the microbiome? We have a lot detail than with IBS..
- ” In fact, patients with celiac disease have a reduction in beneficial species and an increase in those potentially pathogenic as compared to healthy subjects. This dysbiosis is reduced, but might still remain, after a gluten-free diet. Thus, gut microbiota could play a significant role in the pathogenesis of celiac disease, as described by studies which link dysbiosis with the inflammatory milieu in celiac patients.” 
- “children following an African-style gluten-free diet for at least two years were subjected to a change of diet to an Italian-style gluten-free diet for 60 days. Significant differences were identified in the salivary microbiota and metabolome when Saharawi celiac children switched from African- to Italian-style dietary habits. An Italian-style gluten-free diet caused increases in the abundance of Granulicatella, Porphyromonas and Neisseria and decreases in Clostridium, Prevotella and Veillonella, …High concentrations of acetone and 2-butanone during treatment with the Italian-style gluten-free diet suggested metabolic dysfunction in the Saharawi celiac children.” 
- “The main differences were obtained in ecological indexes belonging to the genus Lactobacillus, with significant richness, diversity and habitability reduction in CD patients. In CD bands were categorized primarily with Streptococcus, Bacteroides and E.coli species. In HC the predominant bands were Bifidobacterium, Lactobacillus and Acinetobacter, though the Streptococcus and Bacteroides were lower.”  so CD has:
Jumping to Conclusions
CD has a specific DNA SNP associated with it, FM has a series of DNA SNP associated with it. What if all of these were the same condition (a bacteria shift) — with DNA determining the symptoms/presentations? Where as the conventional 2015 literature cites “The underlying mechanism of the disease is completely unknown and beside of gluten other wheat proteins as well as amylase-trypsin-inhibitor or short chain sugars are discussed as triggers.” 
If this is true, than the IBS probiotics would also apply to CFS and CD. Similarly, other aspects of treatment for the dysfunction described on this site would also apply to CD.
What about wheat free? dairy free? — as stated in the articles, it helps some — why? because it will likely starve some of the bacteria involved (remember there are MANY MANY, see this post on IBS)
Far less studies, with Bifidobacterium having positive results — just like IBS.
- Administration of Bifidobacterium breve Decreases the Production of TNF-α in Children with CeliacDisease.  Note: this was measuring labs only, not severity.
- Double-blind, randomised, placebo-controlled intervention trial to evaluate the effects of Bifidobacterium longum CECT 7347 in children with newly diagnosed coeliac disease.  Note: this was measuring labs only, not severity