Your profile can be either unlisted or private, although members are encouraged (maybe even expected) to not be unlisted. Private has four types that permit you to make either your family tree or your biography or both or neither public, while keeping everything else private. If you make your family tree public then the DNA result you enter will be able to propagate to your ancestors, enabling the possibility of discovering other relatives on WikiTree.
If your parents are living then their profiles can only be unlisted here, which would certainly protect their privacy, but also block DNA results from propagating to (and past) them. To allow DNA to pass through, you can have your parents become members so that their profiles can be made "private with public family tree". They can join, make you their profile manager, and never do anything else here if they don't want to.
Of course, it is completely your choice whether to allow your family tree to be public. Everyone respects your right to whatever level of privacy you feel comfortable with.