If it's a new fridge it's recommended to throw away the first couple/few batches of ice. A filter either before the fridge or built into the fridge on some models will also help.
Do you mean your supply line to the fridge is plastic? Shouldn't affect the taste.....though as with any other new feed system added I'd be sure to bleed it out before hooking it up to the fridge.
Do you mean your supply line to the fridge is plastic? Shouldn't affect the taste.....though as with any other new feed system added I'd be sure to bleed it out before hooking it up to the fridge.