In the first X-Men film, Mystique is able to infiltrate the X-Mansion by disguising herself as a student. She then accesses Cerebro by mimicking Professor Xavier's eyes to fool the scanner on the door, and sabotages it.
But why does Professor X use an eye scanner to lock the door in the first place, since Mystique has this ability? Of course, any security system could be beaten by a mutant with the right ability—like walking through walls or teleporting, both of which are known to exist. However, Mystique is not just another mutant in the Brotherhood. She is Magneto's trusted ally, and Xavier knows this. Furthermore, it is implied that the Brotherhood of Mutants, as an organization, does not exist in this movie—it is just Magneto, Mystique, Toad, and Sabretooth.
So why does Professor X use a security system that is vulnerable to one of his known enemies, and the one most skilled at infiltration at that?