The magnetic pole of the Earth which is located in the Arctic is called the North Magnetic Pole, but it attracts the north pole and repels the south pole of other magnets. This has nothing to do with physics, of course; it’s just a quirk of nomenclature. But one could cite this as a case of unlike poles repelling.
That site looks like utter garbage; there are nuggets of real physics in it, but there are many undefined terms. Also, it relies entirely on the work of Dewey Larson, who may or may not have been a crank (actually, he was definitely a crank, but he may or may not have been wrong).
Darn it, my son was bugging me about his electromagnet and I misread the OP. Ok, yesterday’s experiment, I held a much stronger magnets’s South pole against a weak creramic disk magnet’s South pole. The sum of these fields was a Weaker South pole at the ceramic magnet’s North pole. This is a bit of cheating, but demonstrates how fields add.
There is still a repelling force between the two magnets, but the attractive force is stronger. You can observe this by turning the small magnet around and observing that the force required to pull it away is greater than the force required when the like poles are touching.