I am also pretty familiar with the Koran and although the above does imply that People of the Book should be protected by Muslims and are not enemies, many Muslims would argue that the above only applies if the Christians/Jews are living under the protection of the Caliphate and paying the Jizzah tax.
Ignoring that technicality, if a Muslim is inclined towards waging Jihad and killing non-Muslims they would believe we're in a state of war anyway, with the Christians and Jews waging a war on Islam, so that certainly won't help. Quoting the Koran may make them believe you're a Muslim, but then they can still call you an apostate for not dressing right, listening to music, drinking alcohol etc.
further, there are verses in the Koran that contradict the above, ie the later War Verses, which technically supercede the earlier ones. These call Jews in particular 'rats and pigs' and command Muslims to 'slay them wherever you find them'.