A "furry" or plushie is someone with an interest in stuffed animals. In some cases, this is manifested in a sexual attraction, although this is more the exception to the norm. Still not sure how furry you need to be to get an invitation though. Never, mind...it's probably not important.
Printed copy · Anthology Volume 4, page 980Printed copy from The Tender For Law Anthology, Volume 4, page 980 (printed 13 June 2014). Added by this site; not part of the Facebook export.