Livestock farms, family owned or otherwise, screw with the environment by depositing animal waste into local water ways and by using deisel and fossil fuel for transporting live and slaughtered animals, among other things. Turning an animal into a coat also involves treating their skin and fur with highly toxic chemicals that prevent decomposition, act as pesticides, and condition the fur. Last I checked polluting ground water, manufacturing pesticides, and burning fossil fuels didn't constitute environmentally friendly procedures.
Any industry that deals in the mass production and consumption (and if you're farming something, you're mass producing it) of anything, but animals in particular, is going to have a major impact on the surrounding ecosystem. When you consider that these items are often for global consumption and consider the refrigeration and gasoline involved, the area of impact widens tremendously. Asking how the animal rights movement highjacked the environmental movement misses the point completely. Now do you understand?