set phasers to thrust
They address that in one of the phone messages. Basically they would simply see you as a suit without an exoskeleton and force one into the suit with you inside it which is probably even worse.
Thats not it, the guy says if you play dead, they think your human self is a suit without an exoskeleton. There was no mentioning of a fursuit. And even if so, what if you were to move around, they would realise that there is something in the suit already, but as i said the suit might be giveaway since the animatronics suit appears different to a fursuit.