Comments on fungus. There are many, perhaps hundreds if not thousands, of species of fungus on the planet, and many occur in an aquatic environment. Some are relatively harmless to other life, but many are highly toxic. Without knowing the exact species of fungus, which would take microscopic analysis by a microbiologist, it is impossible to determine toxicity.
Fungus that oozes out of wood may be highly toxic. Grapewood (someone mentioned this earlier) has frequently killed off entire tanks of fish. This wood should be avoided. Mopani wood and Manzanita wood, the blond-coloured or two-toned types, have also been known to contain highly toxic fungi.
I personally would not leave any wood in the tank once it showed white fungus. I lost fish to this myself, and have known of other aquarists having the same problem. If you value your fish, do not risk it.
Last comment on that article; it is very informative respecting fungus, but gives no indication of toxicity. Which isn't surprising, since it requires identification of the specific fungus species to determine this.