What is this fungus-like matter at the base of my Bradford pear?
I suspect as you do that this is a fungus. However, this is a little unusual. Check to see if some sap is leaking from the tree that the fungus is growing on. There may be an infestation of a bark beetle or bird damage to the tree bark that allows the leakage. Sometimes trees "bleed" after they have been pruned at a particular time of year and a fungus can grow in the bleeding sap I don't think that is the case here or you would know that the fungus is growing near a fresh cut and see the seeping sap. And then, the fungus may just be growing there because of all the rain we have had at the end of the summer. Is there mulch around the tree that could be the source of the fungus spores?