If fungi/mold containing grain (let's say barley grain) were about to be digested, how would fungi/mold affect digestion performance? Will it inhibit or will it stimulate the digestion at full scale?
According to my opinion there is nearly no danger for anaerobic digestion from fungi/molds because fungi/molds are mostly aerobic organisms and under anaerobic conditions there is nearly no their activity.
Then fungi probably ate some of the easily digestible components, such as free sugars, which will make the beginning of the digestion somehow slower (we have seen it with moldy lignocellulosic biomass as well). But I agree with Vit Mateju, the fungi will probably die soon after exposed to the anaerobic conditions and will not affect the digestion afterwards.
I will like to add just one more thing to what has been already said (all good responses). If you are considering a flow-type anaerobic digester (the type that produces biogas continuously), you may need a scrubber to get rid of unwanted substances like hydrogen sulphide etc depending on the substrate fed into the digester. Basically, methane is what you need, most others can be done away with. Your need for a scrubber will be better appreciated if it is a batch anaerobic digester you are using.