I find that anti-science people reach their conclusions very similarly, through faulty reasoning. That's why I can group these dumb reasons together, even though those that are pro-nuclear power are of a completely opposite opinion than those who are anti-nuclear power. There are good reasons to be pro- or anti-nuclear power. These are not them. In particular, I'm going to focus on the pseudo-health physics arguments often posed by those on either side of the nuclear power discussion:
1. "Jane Doe, PhD. said radiation is safe (dangerous) and she has credentials."
Credentials mean that a person should have facts that they can communicate. However, often people are wrong about certain facts or have an agenda. Ignore credentials and stick with the claims made, compare those claims to the facts.
2. "There is a conspiracy of scientists (industry) and you are just a shill!"
Whether there is a conspiracy or not is irrelevant. Stick with the claims made. If the claims being made are in accords with the facts, then the claims are substantiated.
3. "You are biased because you have made money on behalf of (against) the nuclear industry"
Someone may very well be biased, but you can't jump to the conclusion that someone is biased. The person has to demonstrate behavior that shows the person is not objective. Compare the claims made by the person to the facts. If the facts support the claims, then the person isn't demonstrating bias. If the facts don't support the claims and the claims are consistently pro- (anti-) nuclear power, then the person is demonstrating a bias.
4. "There is no scientific consensus, these 12 (+/-) scientists disagree!"
A scientific consensus doesn't mean every single scientist agrees with each other on everything all the time. Often, people don't have a full understanding of the science, sometimes they have an agenda (book to sell, donations to be obtained, etc.). If you have fixated on a small group of people (usually because of their credentials, see 1.) you may be in a bubble. Understand factually, why the claims made by those people differ from the scientific consensus. Almost always, the small group of people are in error, whether pro- or anti-nuclear power.
5. "This study shows everything we've thought we've known is wrong!"
It's possible, but highly improbable. We've been studying radiation effects for over 100 years. We don't have all the answers, but any particular study is more likely to have weaknesses, than to be a game changer. Look for those weaknesses before concluding the study has overturned history.
6. "Jane Doe used to be with the industry (environmentalists) and now she's with an environmental group (industry). She is to be trusted!"
Just because someone has changed their mind doesn't mean their claims are in accordance with the facts. Check their claims against the facts. If you find their claims are accurate, they can be trusted. If not, they can't be.
7. "Nuclear power is safe (dangerous)!"
"Safe" and "dangerous" are subjective terms. Define the criteria by which one considers something safe or dangerous. Then compare nuclear power to other sources of energy or any other activity using the same criteria. See where nuclear power ends up in the comparison(s).
8. "John Doe does research in this area and he says X. You don't do research, John is right!"
Doing research is a means of employment. A person can understand a subject without doing research, and someone doing research may not fully understand the subject. If a person (doing research or not) makes a claim, compare it to the facts. What someone does for employment doesn't matter.
9. "The Linear, No Threshold Dose Theory is just a theory!"
In science, a theory is the best explanation which describes all of the observed facts. Don't confuse a theory with a hypothesis (an idea which needs to be tested). "Just a theory" doesn't make sense.
10. "You're an idiot, you're a troll, get lost, etc.!"
If someone is just calling you names, that someone doesn't have facts to support his/her position, whether pro- or anti-nuclear power.