I point out some references
Here they show that angles should be bounded below 180 deg.
This gives a more recent survey.
Nice brief survey, show that maximum angle condition is also not necessary.
Most of this discussion refers to simplicial elements and I am not aware of what happens on quad/hex elements.
For finite volumes, there is so much variety of schemes (e.g., cell-centered vs cell-vertex) that I don't know any general results. But still small angles should not be a problem and in fact, you benefit from using highly anisotropic triangles when computing discontinuous solutions, or those with steep gradients as in boundary layers. For high Reynolds number flows, you have to use highly stretched triangles in the boundary layers which have small angles, nearly right angled, but they do not have large angles.