As I've gotten older, a particular strategy for more illuminating and constructive discussions and debates I have found when someone expresses deeply held hostility or opposition to an idea is, "So what's your alternative?" Not only does this serve as a test of the seriousness of the individual opponent, but it also has the effect of turning the focus of the discussion from being one solely focused upon defending one idea to evaluating the relative merits of multiple ideas in context.
This of course has particular relevance to many aspects (and objections) to the nuclear fuel cycle, especially when it comes to the most serious objections, such as what to do with spent nuclear fuel. For example, a nascent tactic of anti-nuclear activists has been to insist that no solution exists for waste, something which both demonstrably false (e.g., deep geologic disposal - think WIPP or Yucca Mountain, or even deep borehole disposal - is both technically sound and readily achievable, despite being in my opinion wasteful; in addition, strategies such as reprocessing remain immediately viable and advanced reactor concepts and technologies, including thorium-based concepts - think LFTR - are clearly on the horizon) in addition to being entirely myopic.
To wit - if the waste problem is unsolvable, not even shutting down every reactor tomorrow will rectify this, while solving the above problem makes the objection moot. In as much, a good test for the seriousness of the objector's environmental (or other) principles is in whether they are interested in solving the problem or finding a new objection.
The above can be couched as example of the alternative hypothesis strategy in action. If geologic disposal is out of the question, what is your proposed alternative? If reprocessing in unpalatable, what do you propose to do instead? The purpose here is manifold - in addition to testing the seriousness of the objector themselves, the focus is now placed upon the search for a satisfactory solution rather than assuming a defensive posture.
And of course, this applies more broadly as well. Inevitably, there is the objection that nuclear is "too risky." Despite my obvious disagreement, what is your proposed alternative? More natural gas turbines - taking with it both the direct risk to safety as well as the overall increase in greenhouse gasses? A panoply of intermittent energy sources like wind and solar with their attendant infrastructure requirements, high costs, and requirements for backup given their rather limited scale and availability factors? It may well be that no common agreement can be found, given the emphasis different individuals will place upon specific factors (economics, risk, environmental impact, etc.). But putting the problem into the context of evaluating proposals like nuclear energy not in the context of a perfect (and perfectly fictional) alternative but against the very real alternatives available (with all of their attendant limitations) can provide an extremely clarifying aspect to the discussion.