Mishima a long time ago broke from the teachings of the Cardinal. The reasoning behind this was Mishima claimed that the Brotherhood had lost it's validity and was just a group of power hungry individual. They do not have dealings with nor do they openly work with members of the Brotherhood. For this Mishima is often chastised as being a festering pit of herecy.
To handle the influence of the Dark Soul within their borders Mishima had organized the Demon Hunters. The Demon Hunters sole purpose is to seek out herecy and do a fairly good job at it. However since just before the first corporate war another influence of the Dark Soul appeared.
Shadow Walkers are an organization that started with a disgruntled technomancer of Algeroth who destroyed the temple in which he worked with a group of power hungry heretics and then proceded to get revenege on the family which killed his parents and family. To learn about Shadow Walker history and how they came to be so feared as of late click here.