Putting aside the climate change denial nonsense, this is actually not a problem. Biologically sourced CO2 is intrinsically carbon-neutral. The CO2 the fungus is releasing is sourced from plant matter it's using as food, and that plant matter sourced its carbon from the atmosphere. It's a closed loop; there is no surplus carbon being released. If the fungus didn't release the CO2, then bacteria/mold/bugs would have eaten it and released the same CO2.
As a rough analogy, think of a big fish tank with an elaborate water filter. The filter takes water from the fish tank, processes it, then pours it back in. That filter is constantly pouring water into the fish tank, but it's never going to cause the water level to rise; it's not adding any new water.
Cattle is a small problem, they're still carbon-neutral, but a significant amount of their waste is released as methane, which is a stronger greenhouse gas than CO2. It's a temporary problem though, because methane will slowly break down into CO2 in the atmosphere.
Big-problem CO2 is sourced from fossil fuels. This is the stuff that's causing the water level to rise in our fish tank. It was originally from biological sources, but it's been buried and out of the cycle for hundreds of millions of years. Coal for instance came from trees 400 million years ago. Trees were brand new back then, and no life forms had evolved the ability to eat wood, kinda like how right now nothing can eat plastic. It was a totally foreign material that could not rot. It could be broken down physically, but that doesn't release the carbon. So we had vast forests across the earth that would suck carbon out of the atmosphere, grow old, die, fall down, and just lay there, slowly getting buried under sediment. Slowly locking away carbon as the earth cooled.
I guess this was a pretty long-winded way to say mushroom-based CO2 is just peachy.