Never. Perfect physical contact and fluid exchange are necessary. I need her vaginal fluids and she needs my sperm.
Although in theory it can give a small advantage against bacterial problems, by the time the person puts on the condom with his fingers, which he used to caress the dog before, the condom is not sterile either. As soon as the condom reaches the outside of the pussy, it pushes the bacteria in front of it. There are no such advantages. So I consider this "advantage" to be bullshit.
I never use a condom.
But if you have sex with a stranger's dog or that other people have sex with, it's worth it.