Milkweed and ragweed are not listed in the link you cited...nor are dandelions.
I realize that sometimes herbicides/pesticides are necessary for economical food production,
but pretty lawns do not fall under that guise to excuse the poisoning of our planet.
Your argument also does not address the OP's questions and dilemma.
Actually milk weed is listed. Ragweed causes major allergies, so is more of a problem for humans. But there are plenty more dangerous plants, like Hemlock and Nightshade. None of these are likely to grow in your yard if it is mowed regularly, except along the perimeters.
My point is that just because it is a man made chemical doesn't mean it is more dangerous than nature. Animals can tolerate many chemicals because they encounter them all the time in nature.
When I spray 2-4,D it is highly diluted, and spread across a large area. The plants that absorb it into their leaves the most die, so they are not ingested. I assume the grass does not absorb it as well, since it lacks broad leaves, which is why it doesn't die.
I can accept the minimal risk of trace amounts of a chemical only known to be poisonous to broad leaf plants being ingested by my chickens as about .01% of their diet. If you cannot, then don't use it.