Frankly speaking, it's almost impossible due to a few reasons:
1.) If you have to keep arresting and tazing unfortunate fellas, you will see a heap of arrested and unconcious people lying around. If it's a lot more of them, the game will crash.
2.) Is killing the national guards at the first part of the game count as a kill, besides the zombies? There is no clear indication - the game forces you to kill the three poor bastards at the Paradise Dream Bridge.
3.) If you are fast enough, probably you can stop the Fanatics from crossing the Tex-Mex border without getting your karma minused. But lots of them are rushing inside, and arresting/tazing them takes an amount of time. More than 15 of those entering Mexico, game is failed immediately.
I've seen the neutral ending through the Bink Video Player. I'd try to do a non-murder thing, but it's pretty difficult. I hope someone can do a no-kill playthru of the game in Youtube.
