It sounds like your friends might be having a bit of a laugh simply because of aesthetics and because your running shoes do not look as clean and sharp as they once were. As long as it does not bother you, there is certainly nothing wrong with running in a pair of running shoes that look a bit scuffed up, muddy, dirty, or just “used”. In fact, you probably want them to look that way, at least a little bit! Runners find pride in knowing their shoes carried them through tough, dirty, and muddy training runs, over hillsides, and kept them going despite less than preferable weather conditions. You can actually be PROUD that your shoes prove that you have been running (and are not so clean and pristine still that they look like they have not been ran in or used at all).
However, the real problems start to arise if you wear your running shoes for too long and risk injuries. Running shoes do not last forever, unfortunately (though sometimes we treat them as if they do!). Like a car, running shoes eventually get too much wear and tear put on them, and they lose some of their integrity. Repeated pounding in your shoes results in a loss of stability, less cushioning, less support, and too much flexibility in the shoe. When our shoes lose their supportive layers and insoles, it can mean that we risk injuring our feet, ankles, and lower legs through a stress fracture or som either injury that is due to not having enough support.
So, the bottom line then, is that you SHOULD be changing out your shoes about every 300 to 500 miles that you run in them. But that is definitely not once every month! It is more like once every three to six months, depending on how many miles you are running each week. To keep shoes lasting longer and to make your feet stronger, you can swap out between two or three different shoes. Your feet will get stronger when they run on insoles that have different amounts of cushioning, stability, and support. Change is good!