Why do Mr. Great-Heart and the boys cross the stile after being warned by the stone message left by Christian?

The Pilgrim's Progress is a Christian allegory. That means that there's a hidden story in the tale that expresses the Christian message. Earlier in the story, Christian and Mr. Hopeful make the mistake of seeking an easier path on their journey. The path they've been following is hard; their feet are sore and they feel increasingly discouraged. So they decide to walk through the fair meadow parallel to the long, arduous route they've been following.
In order to get to the meadow they need to climb over a little stile. But the fair meadow leads the pilgrims nowhere; it may be pleasant, but it simply diverts Christian and Mr. Hopeful from their journey, and as a result, they lose sight of the Celestial City. Not only that, but they're captured by the Giant of Despair and imprisoned in Doubting Castle.
Bunyan's message is clear. The true spiritual path, the path of Christ, is at times long, hard, and demanding. Inevitably, many people give up and choose an easier path in life. But doing so will simple lead Christians further and further away from the path of righteousness, which must always be followed, no matter how hard it gets sometimes. Christian comes to understand this after his foolish detour.
As for Mr. Great-Heart and the other pilgrims, they hit upon the daring plan to storm Doubting Castle and free any pilgrims there who might be imprisoned. Mr. Great-Heart is certain, that with Honest and Christiana's four sons in tow, he'll soon reduce this fortress of doubt to a pile of smoldering ruins. And he does, but not before hacking off the Giant of Despair's head.
Mr. Great-Heart is Bunyan's idea of what a Puritan pastor should be like: a man who takes the forces of evil head on; a man who doesn't allow his flock to stray from the path of righteousness. This second group of pilgrims has a much easier time of it on their journey than Christian, precisely because, unlike him, they have a redoubtable man of God there to guide them.