Yes you can use Castile Soap for doing laundry.
I sometimes use Castile Soap for laundry when I run out of my regular detergent and it does a good job at getting the laundry clean.
Castile Soap has a variety of uses and if you can use the soap for your skin the soap will also work for doing laundry.
I've also used dish detergent and even shampoo to wash laundry with when I've run out of laundry detergent before and it does the same thing cleaning the laundry.
Although the laundry detergent gives the clothes a better smell after washing them the Castile Soap and other soaps get the laundry just as clean.