Person #1: "I won't put my genealogy information online because I am afraid someone might steal it."OK, now let me add my own comments and questions: All of those records are always available to everyone else. What is person #1 trying to hide?
Person #2: "Where did you obtain all that information?"
Person #1: "From freely available public records, including census records, birth and death records, newspapers, and such."
You may refer to the information you collect as "my ancestry" or "my records," but that doesn't mean that you own the information. In fact, most such information in the U.S. and Canada is freely available to everyone in the public domain. Nobody can claim that data as their own.
Yes, there are exceptions for new interpretations or for any analysis that you create, but the names, places, and dates are always public domain and typically are already available elsewhere to anyone who cares to take the time to look. Since it is already freely available elsewhere, I see no reason to try to hide the information. You certainly cannot claim ownership of names, dates, or places.
I won't publish names or other information about living individuals for other legal reasons, but I have freely published information online about my deceased ancestors. The concept of "protecting my genealogy information" strikes me as laughable, as long as we are not talking about living persons. If anyone wants to learn about my ancestry, or yours, they can do so in the same manner that I did: one record at a time. In fact, I hope they do so and, if they find anything I overlooked, I hope they tell me!
Information about one's ancestry is freely available everywhere in books, microfilms, old records in various archives, and sometimes online. "Protecting" it from others strikes me as a waste of time.