I think the main chip that was linked to an increased cancer risk was a certain brand that emitted radio waves at all times, not just when it was scanned, like most brands. I think that one was taken off the market. I haven't heard of an increased cancer risk being linked to AVID or HomeAgain, but I suppose any foreign object in your body has the potential to cause an immune reaction, leading to cancer. I still think the possibility of losing my dog due to being euthanized in a shelter as a stray is a greater risk than the possibility of a localized cancer.
And, although it's possible that the goverment could obtain the microchip company's record in order to persecute the owners of certain breeds, I feel that this is a very small possibility. There are privacy laws, and if things get to the point where the privacy laws are being completely disregarded, there will be worse things to worry about than breed laws. But to each his own.
And yes, vaccines are linked to cancer. But not being vaccinated is linked to developing diseases

. Although I would use nosodes to "booster" an adult dog, I would not count on them to protect my puppy from Parvo or Distemper.