Comparison of atomic radii
Atomic radii cannot really be uniquely nor accurately defined.  However, there is generally a very big difference between covalent, van der Waals, and ionic radii.  

So, by most any definition of the respective terms the covalent radius of fluorine will be smaller than the van der Waals radius of neon.  Similarly, the ionic radius of fluoride ion will be larger than the van der Waals radius of neon. The reason for the latter is the higher nuclear charge on neon.

However, most sources list a slightly smaller van der Waals radius for fluorine compared to neon, but a slightly larger covalent radius for fluorine compared neon. So when comparing radii you have to carefully specify what kind of radii you are talking about.