That's why you start with so-called "small talk". It's rare that anybody really cares to talk about the weather, or notable local news, or the performance of the regional sports teams. But these subjects are safe. They give your conversation partners an opportunity to give an opinion and hint at their real interests (their families, their hobbies, etc) without broaching subjects that others might find exceptionally unpleasant or offensive.
So, don't "jump from one topic to another that has nothing to do with the previous". Give your conversation partners opportunities to change the subject, in a way that feels natural.