It’s hard to say. Many clothes are produced in China, but the fabrics are from Japan. In 2011, cesium was found in tap water for a while, so everyone bought mineral water to drink. Is it used in the dyeing and manufacturing process of the fabrics? It's hard to tell with polluted water.
After making cloth and clothing, as long as they are not left out in the open, there is generally no need to worry about cesium contamination.
Just imagine the worst case scenario. The clothes you bought were produced near the Fukushima nuclear power plant and were left outside in the open air. In this case, not only would there be cesium on the clothes, but it might also be stained. There are many other types of radioactive elements. The half-lives of radioactive elements vary depending on the type. For example, the half-life of cesium is 30 years, which means that the radioactivity will be reduced by half after 30 years. It can be seen that its harmfulness will last for decades. Like the accident at the Chernobyl Nuclear Power Plant, 25 years later, the cesium scattered on the ground only penetrated 25cm into the soil due to rainfall. Eating the vegetables grown here will bring the cesium into the human body, and it will be excreted from the body through metabolism. Some will stay in the muscles and emit radiation for more than 60 days.
The most taboo thing is that radioactive substances on that piece of clothing can enter your body. For example, cesium is soluble in water and can enter the body through the skin. Certain radioactive elements can enter bones and remain there, increasing the likelihood of cancer and leukemia. But as long as you didn't inhale or eat radioactive materials into your body initially, those radioactive materials would have already flowed into rivers and lakes through the sewers when you washed your clothes, so don't worry.