Is BeF2 Polar or Nonpolar?

Answer: BeF2 (Beryllium Fluoride) is a nonpolar molecule because all of the constituent atoms are arranged linearly around the central atom. 

The bonds in BeF2 would be considered polar covalent due to the great electronegativity difference between fluorine (3.98 i.e. the most electronegative element on the whole periodic table) and beryllium (1.57). The large electronegativity difference is also the cause for beryllium having an incomplete octet both because it lacks extra electrons in its valence shell for bonding and because it doesn't have a high enough electronegativity to form these bonds to complete its octet. This situation is very similar to that of BF3 which is discussed in more detail in this article

BeF2 Ball and Stick Model
BeF2 Ball and Stick Model. Created with MolView.
In fact, this great electronegativity difference gives BeF2 many of the properties of polar molecules. Due to the pull of fluorine on the shared electrons, the central beryllium atom becomes electron-deficient (gains partial positive charge). These partial positive and negative charges allow BeF2 to dissolve readily in water. Furthermore, the partial charges are so strong that at standard temperature and pressure BeF2 is found as a solid (picture below). This quartz structure becomes so strong that is has a melting point of 554˚C and a boiling point of over 1000˚C.

Example of BeF2 quartz. Source
When considering these realities, it is safe to qualify the original statement as BeF2's structure in a gaseous state which occurs very rarely in nature. Typically BeF2 is found in its solid form and thereby exhibits characteristics typically associated with polar molecules. As with any field, chemistry has exceptions and outliers that don't fit the rigid molds and descriptions we try to define. BeF2 is a molecule that certainly would qualify in this respect.