The courts do matter, for legal decisions. They don't have the final say beyond that. Sure, you can use them as a data point, but the requirement for finding someone guilty for a criminal charge is "beyond a reasonable doubt" (aka, there's only a slim chance it isn't true).

Socially, that isn't required. Usually we only care if it's more likely than not. Sometimes, depending on the severity of the accusation, a lot of people have an even lower barrier for taking it into account to effect their opinion of the person. For example, if there's some evidence that someone is a murderer, but not "beyond a reasonable doubt," I'm probably not going to hang out with them, especially alone.