NON-ACCREDITED CURRICULA Spokespersons will tell you that it is not important to be accredited because your child will be able to take the appropriate tests to prove their intelligence. If you choose non-accredited curricula then you can also create your own curriculum or purchase supplements as needed.
ACCREDITED CURRICULA Spokespersons will tell you that it is very important to be accredited because depending on the state, if for some reason you have to stop homeschooling and attempt to enroll your child in a school, you may be denied due to lack of accreditation. Also, most colleges require an accredited diploma so accreditation during 9-12th years is definitely important.
I recommend that if you know many people who have used a curriculum without accreditation in your state with success like Florida, then don't worry about accreditation. But if you think that you may move, or you are not planning on homeschooling till graduation, or want your child to go to any college of choice, or you are just uncomfortable about it, then you should consider an accredited curriculum.