Most scientists laugh most at the notion of a world only a few thousand years old. Since they observed evolution on a daily basis, denial of evolution is pretty much like denial of gravity in their eyes.
Since there are creationists who do admit that the Earth is very old, I would suppose they react most strongly against the evidence for common descent.
What AIG calls "loss of Biblical Authority" is really "loss of Ken Ham credibility." Most of the world's Christians don't accept Ham's new doctrine, which was invented by the Seventh-Day adventists in the 20th century.