In a blender, the obligates will likely die but the facultative will remain.
The problem is that most of the organisms in the gut are obligate (strict) anerobes. Sure the faculatative anaerobes will survive, but this is going to create an imbalance in the populations being transplanted. If the aim is to restore tha balance present in a healthy individual why introduce oxygen when it is easy to avoid.
The other issue is that it would be very hard to get a fecal sample that hasn't been exposed to O2.
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.
If I was doing this I would put the faecal matter in a ziploc bag containing saline, expel all the air, close the bag and gently massage it to get the nice "soup". This would stay anaerobic and save my blender too :)