Is it permissible to initiate greetings with People of the Book and demonstrate the leniency of Islam to them, or should one keep away from them and ignore them, given the permissibility of a Muslim man marrying a woman from the People of the Book?

The ruling is to not initiate the greeting of peace (Salam) with the People of the Book. They can be convinced that Islam is a religion of tolerance and justice (not equality) through good manners, by debating in the best possible way, and by explaining its principles. Not initiating the greeting of peace with them does not necessitate ill-treatment, nor does it necessitate compromising principles or committing transgressions to convince them of Islam's tolerance.