In my last post, Cholestyramine appear as a good supplement based on surveys. Wikipedia describes it as ” a bile acid sequestrant, which binds bile in the gastrointestinal tract to prevent its reabsorption. It is a strong ion exchange resin, which means it can exchange its chloride anions with anionic bile acids in the gastrointestinal tract and bind them strongly in the resin matrix. The functional group of the anion exchange resin is a quaternary ammonium group attached to an inert styrene–divinylbenzene copolymer.” – a description likely above most CFS cognitive ability.
In terms of CFS, R.C. Shoemaker, M.D. first proposed it in his 2001 article on possible estuarine-associated syndrome (PEAS) citing ” resolution with cholestyramine treatment suggests a neurotoxin-mediated illness.” as well as from Sick Building Syndrome , .
- [Chronic Lyme] “Patients coinfected with B burgdorferi and B microti derive measurable clinical benefit from prolonged treatment with atovaquone and cholestyramine”  – 20% became asymptomatic, 64% improved.
On the negative side, 2010 study on a condition that often had fibromyalgia, found “Fatigue was associated with greater use of prescription medication (P < 0.01), in particular for antipruritics (cholestyramine: P < 0.001; rifampin: P < 0.001), proton pump inhibitors (P < 0.002), beta-blockers (P < 0.02), and antidepressants (P < 0.001), whereas those taking calcium and vitamin D appeared less fatigued (P < 0.05).” There are a number of articles on Irritable Bowel Syndrome with Diarrhea.
- “Cholestyramine is a bile acid sequestrant that is generally considered as the first-line treatment for bile acid diarrhea.”
- ” An estimated 70% to 96% of chronic diarrhea patients with Bile acid malabsorption respond to short-course cholestyramine.” 
- “In vitro studies have shown that some bile salts inhibit the growth of intestinal bacteria…the number of ileal anaerobic microorganisms decreased significantly after both bile salt and cholestyramine treatment.” This is good because
- “A significant increase of Gram positive facultative anaerobic faecal microorganisms in 108 CFS patients as compared to 177 control subjects (p<0.01) is presented in this report.”  In other words it appears to counter one aspect of the microbiome shift seen in CFS.
- “Certain organisms such as Bacteroides fragilis are stimulated by bile acids and the activity of such bacteria may be decreased by the unavailability of bile acids bound to the resin [cholestyramine]. Secondly, certain bile acids exert a pronounced bactericidal effect at pH 5-6 and this decreases as the pH rises to 7-2 (Percy-Robb and Collee, 1972). ” 
Bottom line: this is a prescription drug which appears to work well when prescribed, typically for Irritable Bowel Syndrome with Diarrhea. It does impact growth of different bacteria and may shift the population closer to normal in CFS patients.
If your MD is willing to prescribe it for 12+ weeks, around 80% of CFS patients may see improvement. Of course, it would be nice to an actual study on CFS patients with microbiome samples done before and after.