If it's reasonable to expect diet and activity levels to have microbial effects, and it is reasonable to expect the psychopathology in question to have an effect on activity levels and diet; then whatever microbial differences you find between sufferers and non-sufferers could just as easily be the consequence as the cause of the pathology.
Almost like your brain goes, "I'm smiling so I must be happy right now."
If you kick a ball, it begins to roll not only because it was kicked, but because it was round, solid, not made out of lead, etc. Further the presence of the ball may have induced you to kick it. Surely you don't go around kicking empty air.
But we tend to have a sort of simplified view where there is an active cause acting on a passive world to have an effect.