It’s because furries are overwhelmingly queer and often used as a stand in for fear mongering about trans people (ex: the “litter boxes in schools” rumor).
I mean, furries have been targeted by the right for a long time, but they are nothing if not famous for winning the battle but losing the war when it comes to trying to stamp out subcultures they don’t like. They’ve finally given up on trying to legislate homosexuality away, so now they’re turning their attention to a less understood and more marginalized subculture of individuals. They’ll give up on that eventually too when they realize they’ll never win and turn their attention to the next vulnerable group to rally and galvanize their base.
I would say it’s more that they recognize furries are largely a queer subculture (regardless of the fact that straight furries exist) and correctly recognize it as less objectionable to most people’s sensibilities to say you’re getting furries removed from schools by animal control than it is to say you’re getting queer kids removed from schools by animal control.
It sounds really outlandish until you remember that in the 80s, DnD was used to make everyone afraid of a literal Satan, and we ended up with children testifying they were flown across the country and back to participate in Satanic rituals or flushed down toilets into hidden chambers where people were sacrificing live animals to the Dark Lord in the 8-9 hours they were at daycare.
People went to prison over this.