For example, I once reviewed a paper submitted to one of the big two science journals by a famous author at the top of their field. The self-reported statistics made it clear that the data was 95% noise. Although I and other reviewers torpedoed the paper, it was still published at top end paper with the statistics removed.
Nothing like watching the sausage being made to understand why some choose to be vegan. Like soylent green, science is made of people.
The third group is the smallest, but it is not vanishingly small, and addressing your audience as if they "only think they practice science for logical reasons" is itself a social appeal. If you are describing yourself, say so. Don't engage in unfounded anti-intellectualism.
A dilemma: A scientist reasons socially when choosing an area of research. They choose research that will get funded, published, and cited. Or a scientist eschews popular research in favor of something that they think is important, which is irrational on it's face, as that means they won't get funding, published, or cited.
The point is that social reasoning is not irrational. Rational thought always takes place in a frame of reference.
I do not reject rational skepticism. It's an extremely useful tool. It's very good at finding facts. It's very good at convincing the majority of people who reason the same way as you do, and have the same basic foundation of knowledge as you do. It just does not work when it comes to people who do not share that same frame of reference.
It is not a great tool for understanding what is "wrong" with people, or for communicating with people who are wrong. Flat earthers are not wrong because of science, they are wrong because of society. That is, most flat earthers turn away from our shared perception of the world because of some trauma in their lives. They have lost trust in something that they felt was solid.
You may think that you believe in science because you are a logical person, but you really believe in science because people you respect believe in science. Science also has the benefit of actually working, which is nice, but many things can LOOK like they are working (epicycles of the planets, flat earth, miasma theory of disease). You can make scienticious (sic) sounding observations about all of these things.
The point is that when you want to understand why people are wrong, you need to think about motivation and deeply held beliefs, not proof. Scientific proof is obviously very useful, but before you use that, you have to get them to come closer to you.
Imagine a person standing on a hill. If they are shoved and fall down, they roll down the hill. Using the strongest arguments feels like the most effective thing to do. Strong arguments do move people, but you don't get to choose the direction they move.