Both bath towels and kitchen towels can host a lot of bad germs. If you can wash both towels at a hot temperature, it’s fine to wash them together, as this can kill germs. However, always check the care label first to make sure that your dish towels can handle high temperatures.
If you have microfiber towels, they should be washed separately from regular cotton towels. Otherwise, they’ll grab onto lint and other residue, which can lessen their effectiveness.