I think you're right--I was just coming to the same conclusion. I think I want to be using CompareOptions.Ordinal in my specific circumstance. I'm using Compare() to sort items in a list. With the ordinal sort my compares have been consistent.
The comparison call that worked for me was
if (String.Compare(stringOne, stringTwo, CultureInfo.CurrentCulture, CompareOptions.Ordinal) <= 0) { // do things }
Thanks for your help everyone!