If I understand it correctly, people, animals and even objects have swapped bodies, but people still perceive the others as who they are inside. Except for MC's friends who awakened.
MC still sees himself as a gross dude despite being in a girl's body. Dog and woman swapped, so MC sees the dog's mind inside the woman without realizing the dog's body is a woman.
Same for the dildo and the neighbor. The neighbor's mind is stuck in the dildo, and the dildo's "mind" is in the neighbor's body. And MC doesn't realize it's the neighbor's body.