“Shit kickers” can refer to sneakers, as they are certainly the most commonly worn shoes these days. A good pair of sneakers collects stains from various mishaps. They tarnish with markings characteristic of the ground you travel. Holes can form in the fabric uppers at various points that receive heavy friction. Crease marks can form in canvas, suede and rubber where your toes bend. Skateboarders form especially distinct bonds with their sneakers based on their skating technique. The rubber meets the road until there is no more tread left to travel on.
Leather shoes, however, were the original “shit kickers.” The term comes from a pair of old boots that a farmer or rancher could quite literally kick animal dung with and not be bothered. “Shit kickers” started out referring to cowboy boots, various forms of work boots, and hiking boots. From there it spread from the lexicon of rural workers into urban workers. Eventually, it came to refer to any old pair of leather shoes from oxfords and bluchers to loafers and boat shoes. Leather ages much more beautifully than various sneaker materials and has a longer life span. That longer lifespan means more time to strengthen bonds and collect damage. If your favorite shoes have a Goodyear welt that allows them to be resoled then they can endure decades of service.
What differentiates a good pair of “shit kickers” from your dress shoes is the care, or lack there of, given to the maintenance of the shoes. Dress shoes are kept shined and buffed for formal occasions. They’re often stained to keep their original complexion as they age. Shoetrees are kept in them to maintain their shape as they wait in reserve for formal occasions.