I have been watching closely this evening. As well as genealogical I have had an electrical energy company, a local tree-pruning company, insurance ads and a business card company. But all of them are banner ads on the right hand side of the screen, no pop ups, and nothing of a personal nature whatsoever.
Of course, Google ads tailor the subject to the user, but they state - and I have found it to be true - that they make no ads of a sensitive or personal nature.