The F-35 is a plane that relies on safety via stealth, rather than armor. The F-35 fuselage can be dented much like any other plane. The F-35 uses a variety of methods to reduce the its radar signature, most of which revolve around the "skin" of the fuselage - the way the fuselage is physically shaped is meant to reduce the reflection of radar, and there are various paint and material considerations as well.
When at any considerable speed, a bird strike will tear right into the fuselage. Take for example the following picture of a bird strike on a separate military fighter.
When the fuselage is damaged in this way, the radar waves are no longer being strategically reflected or absorbed, and the aircraft becomes suddenly very visible on radar.
