Skepticism and denial
Anyone is initially skeptical about a claim that does not match with their current worldview, but also about any claims that are inconvenient or lead to unpleasant consequences. This is natural. The power of science is to help us understand and often even quantify how justified our skepticism is. If we want an accurate answer, we ultimately have to be willing to accept that it might not be the answer we wanted or expected (read Scout vs Soldier mindset).
As a science advocate, you might want to help others overcome their unjustified skepticism or denial. However, to do this, you have to be very clear with yourself that this is about *helping* someone else, and that it is an activity different from regular 'science communication' in the sense of talking about your cool work or stating your results. Be evidence-based yourself, and read these articles on how to actually make the impact you want:
The social responsibilities of a scientist
Scientists, particularly those at publicly funded universities, have many responsibilities (the 'octojob' post), and being able to choose how much to dedicate yourself to these different versions of your job is one of the great freedoms at least of the tenured professor. However, it is clear that many scientists are vastly underestimating how much other people, including their own students, know about such things as ecology, evolution, systems thinking, the scientific method, peer review, and basic facts about biology, medicine, climate, and history. This has led to more calls for scientists to engage in public debate, talk about their science in small talk conversations, and generally take on the responsibility of communicating the basic principles of rigor in science.