No, there is no significant risk of radiation exposure from a washing machine that would be a cause for concern while you are taking a shower. Washing machines do not typically produce harmful levels of radiation during their normal operation.
Washing machines operate using electrical energy to power their motors and control systems. They generate electromagnetic fields (EMFs) due to the flow of electric current, but these fields are generally of low intensity and non-ionizing in nature. Non-ionizing radiation, such as that produced by household appliances, including washing machines, is considered to be safe and does not pose a significant health risk.
Moreover, water is not an effective carrier or transmitter of non-ionizing radiation. EMFs generated by a washing machine would not be transported through the water to your shower in any significant amount. Water is a poor conductor of the types of radiation emitted by household appliances, including washing machines. Therefore, you can consider showering while the washing machine is running without concerns about radiation exposure.
However, if you have any specific concerns about the operation of your washing machine or other appliances, it is advisable to consult the manufacturer's instructions or contact a professional for further information.