In my personal American experience, there’s a general notion that you need a pickup truck to tow anything; there’s so much marketing about how big tough pickup trucks can tow so much stuff and you really need this. So I think the implication of this post is less of a “fuck cars” and more of a “fuck trucks in particular”
Normal soap should be enough to clean your hands and kitchen tools. I believe the issue with rinsing chicken in the sink is that the water can splash little droplets around very easily, and those droplets can have the chicken bacteria in them, thus spreading bacteria around your sink area.