Experiments
We assume it matters what we believe about freewill. This is a testable idea. Let’s get some people, try and make them believe there is no free will, and see what happens.
This is how psychologists think, and there is a mini-industry of experiments like this. Some have shown that people told there is no free will behave less morally - they are more likely to cheat on a test, for example - but others results are contradictory.
Christian Jarrett has covered the are well in his BPS Research Digest post: Contrary to popular psychological theory, believers in free will were no more generous or honest.
Some people have written as if the philosophy of free will is a kind of dynamite - an explosive risk for our moral behaviour. If we believe free will is dead perhaps we are not responsible for our actions and everything is permitted.
My take on this is that this is a flaw in our intuitions about responsibility, not because there is a terrible truth about our (lack of) free will which we must be protected from. Your choices are yours, regardless of how free they are as a choices.
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Causation isn’t the same as responsibility CAUSATION; direct link causation