You can't shoot through the shield no. Unless you place teh shield so teh end of teh E-web or MK2 stationary weapon is popping through it (a gameplay mechanic we want to keep).
Grenades do not go through teh shields. they are an extremely good defensive strcture. HOWEVER. as previously said there is a counter. and that is the medi'c Bio warfare Poison Grenade.
It is the only (so far) weapon available to penetrate teh shielding, which increases the usefullness and teh need for a medic class (we have many gameplay mechanics that necessitate certain classes/weapons, all to encourage situational based gameplay)
throw in a couple poion gas grenades (biotic grenades) and you'll see the enemy scatter from behind their shielding giving you a chance to take them out.