Mushrooms are the fruiting bodies of mycelium.
If you are seeing fruiting bodies, you have mycelium somewhere.
Mycelium can live in different mediums depending on the species.
Its safe to say that it is growing in either the dirt, or on dead wood in the dirt, or both.
Changing your soil would obviously get rid of the issue.
Most organic soils will have some sort of mycelium growth in them when purchased.
You can sterilize the soil, by placing it in mason jars, and pressure cooking it. Then, so long as no other mycelium is introduced, there will be no more mushrooms.
Plenty of mushroom species are toxic, and plenty are undetermined to be either safe or toxic.
So it is a good thing to keep them out of the enclosure.
Some species may grow in fairly dry conditions, so it may not be just a factor of your overall humidity being too high, but making sure things dry out well, especially at night will help control fungal growth.
(I believe Xanthoman has a more in-depth "tutorial" somewhere for the sterilization of soil, but Im unable to find it at the moment.)