Are Shingon Buddhism, Taoism, and Shintoism seperate or merely permutations of eachot

I am a 3rd year student @ U of Toronto, several professors have related the same concept with different explanations. I was first told in first year that Shingon Buddhism was an esoteric form of BDH that had ticICCnd Shinto features. Another time I was told that Shingon Buddhism was heavily influenced by Shinto folk magic which itself was influenced by Taoism. This last time i was told Shingon was basically Taoism with a Buddhist Shell. Can Anyone Clarify this? I am relatively well-versed in Shinto,buddhism and Taoism, but this has stumped me. Also if anyone can clarify the relationship of shinto and taoism further (besides their obvious characteristics)...And furthermore Taoism is often described as animistic by academia, is it animistic or Pantheistic and thus how would you define shinto besides a nature-based religion? THANK you in advance

Separate, but, you can practice all these religions simultaneously.

They are all of shoots of Hinduism

edit: I don't understand why I got a thumbs down...Far eastern and Asian philosophies and belief systems ARE to an extent heavily influenced by Hinduism.....True Hinduism is about meditation and wisdom, not animal worship.

Taoism is actually atheistic, as it does not buy into the existence of deities except as symbols of abstract ideas.

I think the three have much in common, but that does not make them permutations. They had different sources, that's how you can tell.

The three religions mentioned in your question are all three separate !