Traditionally, people with scalp conditions have been told not to dye their hair, and it is true that certain dyes can be very harsh on the scalp, especially if you have any open lesions.
That said, there are many people with psoriasis who do dye their hair, As with anything, it's all about figuring out what works for you.
It’s probably best to go and see a hairdresser the first time you dye your hair, and explain your condition. They should have knowledge of what products are out there, and can do a patch test to see how you react to the dye. If all seems OK, then dye away! But use caution - some coal tar shampoos can cause blonde highlights to take on a green tinge, never a good look! If in doubt, check it out with your hairdresser or your doctor.