The Bible says that “there is a way that seems right to a man but it leads to death,” and that without God leading us, “every man does what’s right in his own eyes,” which always leads to us going off the right path somewhere.
The Golden Rule in Christianity, then, also requires people to depend on God to find out what’s true and good. He gives us the Bible to teach us, and then His guidance through things like prayer and the words of other believers.
And performing the Golden Rule shouldn’t lead to the chief sin of Satan, pride. Doing right has a great many benefits, and God has suffered long with us to make us able to do good. Giving to charity, if out of pride, can lead to people feeling they have a license to sin a little, convinced God needs them, and they’re so good they don’t need His mercy and forgiveness.
The story of the Good Samaritan is an example of a person living by the Golden Rule.
The point is that if people around the world, whoever they might be, acted with respect and kindness towards others, (as described in the article), there would be far less mayhem and slaughter going on in the world.
And I don’t think anyone can say that would not be a good thing.
Regarding your point about some people thinking, for instance, that other people should be allowed to have abortions because they want them, that is a good point. There have to be moral absolutes accepted, and since all religions basically have the same moral absolutes*, if people actually followed their scriptures (as faulty as many of them may be in various peoples’ estimations), at least they all hold to the same basic moral absolutes.
*I leave Islam out of this because it is vicious from the get-go.