Are all fans fanatics?

Fan is described by most major dictionaries as a short form of the Latin fanatic, which was first widely used in English in the mid 16th century. 

Fanatic originally meant sacred  [Latin fanum, poetic English fane]. The modern sense of "extremely zealous" dates from around 1647. 

The use of fanatic as a noun meaning a temple or sacred place. dates from 1650. 

Divinely inspired?

The term "fanatic," meaning "marked by excessive enthusiasm and often intense uncritical devotion," comes from the Modern Latin fanaticus. This is usually translated as meaning "insanely but divinely inspired". 

That seems a little strong for the supporter who buys the t-shirt but stops short of the facial tattoo.

Are all fans fanatics?

For non-fanatical fans, there is an alternative etymological route via the verb to fancy, meaning "to take a liking to." 

1540s, a contraction of fantasien "to fantasize (about)," from fantasy (n.) - see here.