Is it possible for missionaries to preach without implicitly tearing down others' beliefs?

It depends on the doctrines the missionaries teach. Take Mormon missionaries, for example. Say they tract into a Catholic home. They teach the doctrines of apostasy and restoration, two of the main beliefs of The Church of Jesus Christ of Latter Day Saints. Implicit in that teaching is the concept that the Catholic Church is apostate Christianity that has no priesthood authority (or power) to save. Implicit is the idea that baptisms performed by the Catholic Church are without efficacy and redeeming value. So, yeah, it is possible for missionaries to not explicitly tear down others' beliefs (e.g. The Catholic Church is an abomination), but by teaching positive truths (or what some believe is the truth according to their faith) if their truth contradicts another persons' beliefs than it is not possible to avoid implicitly tearing down anothers' beliefs.