The zombie apocalypse is a popular topic into today's pop culture. (Yes, I know that sentence was redundant.) I am going to address that topic.
I shall first address the question of whether it is morally acceptable to kill a zombie.
The answer is, of course, yes. First of all, zombies are already dead. Second of all, it is always morally acceptable to kill to protect either oneself or the innocent if no other option is available.
Now I shall address what would actually happen in the zombie apocalypse.
First of all, there would be few, if any, casualties, as the majority of humankind can move faster than the plodding zombies. The situation is akin to my distaste, bordering on phobia, of worms. They are ugly, disgusting things and you could say I fear them. Nonetheless, all I have to do to avoid contact with them is to watch out for them, and, when they come too close, simply to move out of the way. The situation would be the same with zombies. The person currently under zombie attack would certainly be afraid of them, but could in actuality go about his business, occasionally sidestepping the zombies when they come too close. Of course, you might question what would happen if the human had got himself cornered. One of two things could happen, operating on the assumption that the human in question is left to fend for himself. The first outcome is that it would be one of the few casualties, and the second outcome is that the human in question, with the energy and strength caused by the natural bodily release of the chemical adrenaline in situations of great fear, would barrel his way past the clutching zombies blocking his way to freedom.
The situations and outcomes above described are that which would happen before government interference with the situation. Once that happened, the zombies would quickly be rounded up and put into a secure area where they could harm no one. Even if there was no organized government at the time of the apocalypse, there would be bands of humans united under the common need to contain the zombies before they wiped out humankind. These bands might even contain the situation faster than the government would, since they would have no bureaucratic hoops to jump through. And lastly, addressing what would happen if there was no end of bureaucratic loops to hamper the government's response, there would be at least a few high-ranking people who would take care of the situation, even at the possible loss of their own lives as punishment for insubordination. They would, of course, take action under the logic that if they continued to let the zombies run rampant, they would die anyway.
In conclusion, even if the zombie apocalypse were to happen, humankind has nothing to fear.