Even though the term contains in it the word "fag" (a derogatory term for "homosexual,") it is not usually intended to imply anything about the target's own sexuality.
It's important to note that although "furfag" contains the word fag, all furries are furfags, regardless of sexual orientation.
anon says GO DIE
furfag says OMG FURSICUTION ITS PERRFECY OKAI TO LUV ANIMALS AND TOUCH THER PENISES
anon says GTFO