The Pilgrimage of Grace was a rebellion, and any rebellion would have been regarded as a threat to the governing body. However, the Pilgrimage of Grace threatened the monarchy for several political, social and economic reasons (though mostly political).
The rebellion lasted for some months and had managed to sweep aside the forced that the king had sent against it. It is seen as the largest and most organised rebellion of the 16th century. One of the most significant reasons that the rebellion threatened the monarchy was that the King relied on the gentry to gather an army when he needed one, and since it was the gentry that instigated (if not led) the rebellion, Henry could only raise 8000 assorted soldiers in response to the rebellion’s 40,000 men. Furthermore, the rebellion was a mass movement under the excellent leadership of Robert Aske and due to the impressive geographical extent of the rebellion it could easily defeat royal forces.
There was large scale dissatisfaction with the regime which put the King under a great deal of pressure to negotiate. The negotiated settlement in both October and December represented a massive climb down for the government. Since Henry was, to some extent, at the mercy of his people, his reputation was under threat. The rebels took control of the north with considerable ease in just three weeks, and none of the local ruling class wished or dared to oppose them posing further threat.
Also, there were several ecomic reasons as to why the rebellion presented a threat to the monarchy. Henry VIII was ill-armed to resist such an all-embracing uprising. He had no standing army, but had to rely on the loyalty of peers like Norfolk and Suffolk to raise troops. This was difficult as Henry was unwilling to spend money. In addition to this, it threatened the stability of the kingdom and hindered local government and revenue raising.
In conclusion, Henry would have been threatened largely by this rebellion because he was ill-prepared to face such a large uprising by men he would usually rely on.