Antibodies are similar in many ways to enzymes. They depend upon molecular shape to lock onto a specific substrate. In the case of antibodies, they are produced (by the presence of specific antigens) to lock onto specific proteins in the coat of the invading virus.
The measles virus will have coat proteins that are totally different from the proteins in the coat of the unrelated chickenpox virus so any antibodies that were stimulated to develop and attach to the proteins in the coat of a measles virus will find no suitable docking station on the surface of a chickenpox virus and will thus be unable to disable it.
Sometimes related viruses will have some identical proteins and thus antibodies stimulated to attack one, will also be effective in attacking the other. Such an axample is the similarity between cowpox and its relative chickenpox which Jenner exploited in the vaccination of humans against smallpox by exposing them deliberately to the less serious disease, cowpox.