I am a donor at a large center performing these procedures and work with the physician and lab staff. The purpose of the blender is to make the fecal material into a slurry, after that it is filter through paper to remove food particles. The filter paper allows the bacteria to pass through. The resultant liquid is given to the patient (enema, NG tube, pill).
Microbiologist here - the name anaerobe is a pretty broad term. Within the gut there is going to be obligate anaerobes (killed by atmospheric O2) and facultative anaerobes (can survive in both oxygen rich and oxygen deplete environments).
In a blender, the obligates will likely die but the facultative will remain.
