Anyons are pseudo particles. They are waves in a 2D electron cloud, but their wave functions are just like the wave functions of traditional particles. They even exhibit quantum entanglement. Quantum computers are even being proposed using not real particles but these pseudo particles.
This is akin to realizing that waves in the ocean are not the water, but the energy traveling through it. The waves are pure energy following a mathematical construct acting upon a local medium. The local medium can be measured, but the wave itself cannot be without a local medium to affect.
Without even getting into faith issues, one realizes our brains are a medium for electrical and chemical waves of activity. That makes our consciousness like the energy behind the ocean waves – mathematical constructs acting on a local medium.
Others have argued that the universe is an illusion of our senses. Thinking of ourselves as abstract mathematical constructs only able to act on another medium, perhaps the universe is not the illusion, we are.