I am also a microbiologist (my Ph.D was in molecular microbiology). I didn't work on obligate anerobes, but the lab next door did. They had to go to a lot of trouble to keep oxygen out of all their experiments by using aneroboic chambers and the like (a total pain).

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.

Two things, you aren't necessarily trying to achieve the identical balance. Most of the research in this area is finding the particular bacteria that are important to repopulate the ill gut. The aim is to eventually transplant only the important bugs or just grow the important ones and skip the fecal donors all together.

The other issue is that it would be very hard to get a fecal sample that hasn't been exposed to O2.