I also suspect the Tom's may kill the white Tom's but have not witnessed this.
Have never seen a wild white turkey in my area.
That said, it still concerns me that the white ones are being killed by turkeys of color. Therefore I am starting a new movement called WTLM, White Turkey Lives Matter.
After receiving sufficient funds for organizing, advertising, etc., we will march on the game departments of every state and demand protection for these poor unfortunate birds.
Please PM me for info on where to send donations!