With such a broad definition, it’s helpful to be clear about what animism isn’t.
The Occult Traditions
Occult traditions like Kaballah, the Masons and the Western mystery schools are not animism. Instead, they are often magical systems close to more well known religions.
They have organised structures and a fixed approach that is consistent between practitioners. They also tend to have a series of tools and methods which students progress through.
However, the occult traditions do use (and often keep alive) tools that are grounded in animism such as spirit communication and spiritual healing through prayer. They often work with symbolism and sacred space, like animism, but in a more structured, less individual, approach.
Mysticism is often very close to animism, and sometimes the only distinction I can find is a more inward looking, less practical, approach.