It's not unheard of ( http://en.wikipedia.org/wiki/Dogs_in_warfare ), after all, people routinely take their best friend into war.. so taking "man's best friend" makes plenty of sense.
That said, my office is in a no-pets building, and I'm happy for it. It makes it a non-issue.
Your war analogy reminds me of a comment a startup CEO once made to me: "A startup is a war. I am at war, and if one of my men can't keep up I will shoot him."
I had great success generating extra interest in an open position for a senior software / CTO position by advertising that we had a "dog friendly" workplace, and that I, the CEO, would be delighted to walk the dog during the day.
Running a startup should be like going into a war about survival -- do you bring your pet dog to the war?
Yours, Insensitive Clod