It should be readily apparent that I consider these two ideas--reincarnating backwards into animal bodies, and parallel lives--as reincarnation "heresies." They have the same effect that distorted teachings like "one life, heaven or hell" in Christianity have had--they water it down and make it look nonsensical to the general public, who then dismiss the entire package as nonsense. Seemingly innocent, they also can cause suffering in future generations (as "one life, heaven or hell" has done), and the entire issue of distorted teachings shouldn't be taken lightly. Swami Vivekananda compared the world to a curly dog tail--straighten it out, and it will curl back up again. So these kinds of misunderstandings or skewings of the genuine spiritual masters' teachings are probably inevitable. Perhaps they even have their place in the scheme of things, in the long run. So, while it is uncomfortable to see the movement one has identified with being degraded or threatened, the spiritually mature response, in my opinion, is, as Krishna teaches in the Bhagavad Gita, do one's best to counter them and then leave the results to God. Becoming hateful, in defense of the pure teachings, is itself an error.
There is a tendency on one side to try to codify and crystalize ideas into dogma; and then there is a reactionary tendency toward exploration and free-thinking. In-between and transcending these two opposites is a fluid, living search for Truth as it manifests downward into various intellectual ideas; and that search is conducted with a balance of head and heart, using both intellect and intuition. When one falls in love with Truth, one recognizes it here, and one recognizes it there. (A man loves his wife--and he will recognize her whether she wears jeans, a business suit, or a Halloween costume.) So what I am saying about the concept of parallel lives, is not that I am trying to fight one dogma with another dogma. I am saying that intuitively, I feel this idea is going askew from Truth. Put simply, it doesn't feel right to me. Then, I go in behind that intuition and try to explain why I think that based on my best intellectual understanding of the teachings given by the spiritual masters I have identified as being authentic.