I live in coastal Texas, and I get this stuff growing in the lower layers of my compost that I believe is some kind of fungus. It is a tangle of long thin runners that clumps up the composting material.Doesn't happen if I turn the piles frequently, but as I get older, that's becoming more difficult.
Should I be concerned about this? Is there another way to eradicate it?
If they are fairly fragile and break off easily, then I agree it sounds like fungus. Don't worry! Its part of the ecosystem. There's tons of fungus out there and only certain ones that make plants sick. Let you compost get fungus if it wants. It'll go away as the compost rots down to humus.
(If they are wiry and tough it could be tree roots, or grass runners.)