What is the best strategy to confront Non-Buddhist ideology?

I am sure everybody in this world thinks that 'my religion is the only true religion' etc and its variables. As we live in a diverse society, in today's age of information we invariably bump into people or places, online or offline, with ideologies which totally contradict Buddhist beliefs. What is the best strategy to deal with such situations? Should we keep silence and ignore and let them live in their ignorance or should we confront and try to explain the Dhamma to them? In the latter situation, it always ends up in heated debates about the existence of god and its near impossible to explain a non-Buddhist that soul doesn't exist and that self is an illusion. What do you do?