There are ways to attend a Ren Fayre as a goth, and be period. Even to work a Ren Fayre and be period.
Unfortunately, it's difficult for peasants.
Nobility have it easy. They can afford to wear stylish clothing cut in the Spanish style, with lots of black and metallic lace; the women can wear white face paint, because it's period, and even lipstick - noblewomen could get away with a little rouge, whereas commoners couldn't wear makeup because it was too tarty. Even the men were pale. In Elizabethan times, the sunlight was considered very unhealthy - Londoners cowered indoors. The only people who got fresh air and sunlight were peasants.
Scholars were often melancholic - dressed in dark colours, gloomy, disposed to philosophizing, lethargic. Melancholia was to the Elizabrthans and Jacobeans what the Goth movement is to today's youth (and was to the youths of the Age of Sentiment, the first "Goths" other than the barbarian invaders of Rome to call themselves Gothic, or at least their culture Gothic). Melancholia was actually much more popular than the goth movement; it was de rigeur for students and for idle courtiers. There weren't many ways of rebelling in the English Renaissance. You could call yourself a Catholic, maybe, but that was dangerous, especially as the Protestant extremists gained power in the court. Melancholia was safer. Part of being melancholic involved dabbling in the occult, if you were scholarly; in Oxford and Cambridge and the Inns of Court, students held seances to have illicit fun about as often as students in American state universities smoke pot or get other recreational drugs today, including indulging in binge drinking. Not everybody did it, but it was still extremely common.
Therefore, anybody who is of at least merchant class can dress up in gloomy black clothing and white face paint and talk about the occult.
Peasants have it harder - probably the best thing a peasant can do is exhibit a paranoia about evil spirits. Coming out as a witch is not a good idea, any more than coming out as a fairy or anything else weird - witches, fairies, etc had a tendency to be hunted down in those days, remember.
It is also a bit difficult to play a vampire. A melancholic person who suffers from "love melancholy" (according to the scholar Marsilio Ficino of the fifteenth century) will exhibit signs of what we today call "psychic vampirism" - because the victim has given his heart away and must borrow life force from other people if he is to survive. Until the loved one gives up their heart in exchange, the victim will waste away from love sickness. Sidney's poem "My True Love Has My Heart, And I Have His" thus takes on a somewhat sinister meaning. It was actually written about what was considered a medical phenomenon.
That sort of vampirism might have been accepted, but it wasn't considered or called "vampirism." Folkloric vampirism was almost unheard of in the British Isles, aside from the leanan-sidhe, which was not called a vampire either; really, there are an awful lot of vampiric fairies (Jenny Greenteeth, et al) and witches who engage in cannibalism before kissing the Devil's arse and so on, but the vampire as we know it is not at all period. It is a modern revision of an Eastern European legend, as revised by Bram Stoker, Sheridan La Fanu, et al. Vampires were popular in the Romantic and Victorian eras but not in the Elizabethan period as such.
If you want to be a vampire and fit into the Ren Fayre atmosphere it would be best to do so discreetly. You don't want to be hunted down by an angry mob.
Also, if you want to be period, it would be best to wear period clothing and to carry a parasol to keep the sun off your face. SPF 200 Sunblock hadn't been invented yet, nor had Ray-Ban's. :)