Make better science.
The act of being a scientist is the commitment to the scientific method, a series of hypotheses, tests and re-evaluations. When you make better science, the scientist's previous opinion doesn't matter, not if she's being a scientist.
On the other hand, if you want to win an argument with someone who refuses to act like a scientist, making better science isn't going to help you very much.
The person you're arguing with now (who might be a scientist during the day, even, but is merely being a person right now) is not going to be swayed from a firmly held opinion by your work to make better science. It's more likely that it will take cultural pressure, shame, passion, humor, connection and a host of unreliable levers to make your point.
This disconnect is why it's so frustrating to encounter people with deeply-held pseudo-scientific beliefs about things like whether or not to support your project. It certainly feels like better science and the relentless power of the scientific method would be sufficient to help them get things straight, but they fail because, in fact, there's no science happening here.
Anecdotes, non-falsifiable premises and most of all, a willingness to change tactics if it helps maintain the culturally-enforced norm are all hallmarks of a non-scientific point of view. In other words, the sort of thing humans do all the time.
The easy way to tell the two varieties of argument apart is to ask, "what evidence would you need to see to change your mind about this?"