I shoot through the mesh. Doesn't mess with my depth perception, but on a few occasions, the netting has accentuated a bad release by contributing to bad arrow flight.
I hunted without the netting years ago. Turkeys didn't seem bothered by it, but it's then necessary to wear a camo face mask inside, and you need to be more careful about movement. Though I don't hunt deer out of pop ups, a few deer that came by while I was turkey hunting seemed to shy away. Don't know if it was because of the dark windows, or if they just didn't like the blind. I don't brush it in much for turkey, and it's fairly exposed.