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 :)
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.
Interesting idea though. What happens if it goes wrong?
Actually the risk of getting worms is an interesting potential positive. There is a lot of data suggesting that the lack of intestinal worms in western countries is one of the reason for the rise of autoimmune diseases like Crohns. The theory is that the immune system in the gut is designed up to keep worms under control and in their absence starts attacking things like the gut tissue instead. There are a couple of stage three trial currently running that are giving people pig wipworms (they can infect but not reproduce in the human gut) to treat Crohns. The earlier trials were really encouraging so it will be interesting to see how they turn out.
But the more I discover about medicine and biology, the more I realize how much we still don't know. Hundreds of types of bacteria in a typical stool sample? This is amazing! Whole biomes await study... from internal gut bacteria (very small scale), to microbial colonies (regional or national scale) that we use for fermentation. Exciting!