Yechincally, compost mulch CAN be used in place of "regular" mulch. I have only read of two disadvantages.
First, it may make the shrubs grow much more tender growth than normal, which attracts insects like Japanese Beetles so the shrubs may show more insect damage. Those pests are not a problem here in Texas so I could use it all over the garden if not for disadvantage #2: regular mulch prevents weed growth and compost mulch promotes weed growth. Since weeds are a problem where I live, I use regular mulch.
I do recommend using mushroom compost as a lawn fertilizer. You can apply mushroom compost as mulch or to the lawn but stop on or after July to prepare plants/lawn for winter.