It is possible to make something that looks like wool, either with plant materials or, more usually, petrochemicals.
Cotton and linen, two common plant-based yarns, can look the same but are cooling rather than insulating, flammable rather than inflammable, heavy rather than light, and liable to stretch irreparably rather than keep its shape. Other plant-based fibres such as viscose and ramie (e.g., bamboo, sugarcane, cornsilk) are similar. Their production, and that of cotton in particular, is also rather bad for the environment.
Petrochemicals, such as acrylic, are sweaty, very flammable (and melt into your skin when they do, which is oodles of fun at the Burns Unit), appallingly bad for the environment for centuries, and are only “easy care” if you wash them on the same cycle as wool – and even then, they shed microplastics into the watercourse and thence to rivers, lakes and seas.