I think the Golden Rule is more of a big-picture starting point for
morality and the other rules being discussed are ultimately subsumed within it. It's starting point is a general one of reciprocity in regards to respect and empathy.
Because
I would like to be treated as an individual and not as just a member
of some group or stereotype, I extend the same to others. (i.e. the
Golden Rule)
Because I realize individuals and cultures are
different from my own, hence expressions of empathy and respect may be different, I take that into consideration and hope they do
the same (i.e. the Golden Rule).
Because mental problems, very young age or mental handicaps exist in all cultures, I would take that into account if I encountered it, and hope others do the same with me. (the Golden Rule).
Because people don't and can't know every person or culture without finding out about them, the Golden Rule is offered as place to start. It has the advantage of being recognized/practiced in some form in most cultures and religions. Once you know a person or people better, you can move into more specifics and treat people in ways they like because that's how you'd like to be treated, as individuals. (the GR again.)