In X2 we see an aerial battle involving some U.S. fighter jets and the X2. Storm and Jean do everything they can to get away from the jets, and end up having to take them down. However, we know from X-Men, and X-Men: The Last Stand, that the X-Jet has an invisibility cloak; why not simply engage this, rather than endanger US pilots and having an aerial battle over continental US?
According to the film's official novelisation, Kitty Pryde seems to have been responsible for developing the stealth technology being used to conceal the plane. In X-Men and X2 she's still just a student at the school, hence why it wasn't installed into the jet until X-Men 3: The Last Stand.
Cute little gizmo, he discovered, in keeping with its creator — full of surprises — it contained a miniature version of the holo-projection systems in the Blackbird and the Mansion, allowing him to view the target area in three dimensions rather than as a flat picture on a screen.
For the record, in X-Men 1, there was no use of stealth technology. Storm created a fog to conceal their approach.
“All right,” Cyclops said, “there’s the bridge. I’m taking us in. Storm, some cover please.”
“You got it,” Storm said. Her eyes went milky white.
As if to mirror those eyes, below, around, and under the G.W. Bridge a cloud of fog began to form over the calm, cold water. Cyclops watched as it began rolling down the Hudson River, past midtown Manhattan, then out toward Liberty Island.