Yes. You can use lists to restrict their access or even exclude them from individual posts with the audience selector if you think you need to, but the reason you need to friend your parents (and siblings and other close relatives) is so they will have access to view your page if you die. Yes, I know you’re not supposed to die before your parents, but it could happen.
This also applies to any other family members or friends that would want to read your memorialized page after you die. One of my more popular posts is What happens to a Facebook profile when someone dies? Most people don’t realize that any friend that has your email address can send Facebook a link to your obituary and get your profile memorialized. Once that happens, your profile is restricted to your friends and no one else can see anything on it, including your Mom. One way to get around this might be to give your password to someone you trust, so that in the event of your death, they can send out friend requests to your immediate family before your account is memorialized.