As far as I can tell gunners of the Old Man M2 turrets are immune to damage from explosives. The turret itself is not, which means that you can kill both the gun and the gunner with a big enough boom, but small explosives like grenades do nothing to the gunner. And if you have an invincible turret, the gunner can take absurd amounts of explosives without taking any damage.
The gunners do take damage from bullets as expected. This issue appears to affect all M2 variants, but does not affect the Mk30 turrets or the M2 technicals. It also occurs both for AI and player gunners.
Video of this issue: https://www.youtube.com/watch?v=G3L4vG64yHs&feature=youtu.be Note that the turret is *not* invincible here; as far as I can tell the APERS mines just don't damage the turret, probably because they can't overcome its explosive resistance.
Testing done on main 1.98.146373, in local "multiplayer", with no mods or optional DLC.