by Why does my shower back up when I run the washing machine?
Short Answer: The combined wastewater flow may be overwhelming a restricted drainage or septic system.
Detailed Answer: Washing machines discharge large volumes of water quickly. If the septic tank, filter, pump, drain field, or sewer line is partially restricted, wastewater may seek the lowest available exit point, often a shower or floor drain.
Related Questions: Can washing machines overload septic systems? Why does wastewater return to lower fixtures first? What causes septic overload?