Every holy place of every faith has its own etiquette. When Pres. Clinton, Pres. Obama, Pope John Paul, Pope Benedict came to pray at the Western Wall they covered their heads. When married women come they cover their hair and all women dress modestly. In church men uncover their heads. In mosques people remove their shoes. On entering any holy place you accept its own rules. It's just common sense and respect.
Woman moderately wounded by firebomb thrown at her car in north J'lem (Haaretz)
from the article: Police arrest woman for wearing prayer shawl at Western Wall