Lack of political sophistication is often a side effect of being sheltered. Of course, the truth is that politics is weird and wild and wooly, and there are more corners to it than most people will ever be able to imagine. (Try explaining the concept of accelerationism to someone who thinks Obama is left-wing.)
In this sense, our best weapon is mere exposure. Even without attempting to remain civil, and even without bringing up views we necessarily believe in, just exposing people with a limited understanding of the range of political ideas to positions outside their mental models is helpful.
If someone is pushing an extreme view, push a view you see as extreme in the opposite direction, so that the overton window expands rather than shifting. Expose fascists to anarchocommunism. Expose neocons to negative taxes and neoliberals to deflationary currency. Expose right-wing transhumanists to anarchoprimitivism.