do good stereotypes always have to send out good messages towards those good people?

Answer 1

No. Any stereotype is likely to injure people.

For instance, think of Asian students in Canada or the U.S. The stereotype is one of a very bright, mathematically gifted nerd. But obviously some Asians are of average intelligence and don't like math.

Answer 2

stereotype: an over-simplified image

So what is a "good" over-simplified image?

It boils down to your value system: good vs bad. What one values as good another values or knows differently.

Think about Beaver Cleaver's mom June
http://en.wikipedia.org/wiki/Theodore_Cleaver
was the over-simplified role of a housewife and mom a good message? Ever hear of the glass ceiling?

So the answer is your opinion of "good".

I am reminded of the Holy Crusades, and the knights who went on them? I am not so certain the messages they left are considered good by all.