Are you on a bike or walking? If you are walking you might care, but on a bike it poses an interesting question. As far as I know, they are not regulatory, but informational. For example, if they flash don't walk it really means don't start across if you haven't left the curb. If it is solid I would say you can still go, as long as you are out of the intersection before the light changes.
I've had motorists yell at me for walking when is was a solid don't walk or flashing (I ignore them, as they shouldn't be navigating an intersection and deciding whether or not to violate my right away via the walk signal). Regardless, I have the right away. The signals follow all kinds of weird sequences so I go off the traffic signal (if it's green I go). I've seen one side of the street with white walk and the other solid don't walk. Talked to the traffic engineer and he had an explanation, but it didn't make any sense. Just confusing to the per. No wonder why people don't walk much.