On lay society? Probably not very much. Most people couldn't read, and certainly didn't feel obligated to follow the Rule.

On monastic society? It was hugely impactful. It was the most popular monastic rule for a long time, at least until the Franciscans, and for people who follow it, it governs every aspect of their life.

For one example of how the Rule works in daily life, see the Chronicle of the Abbey of Bury St Edmunds. The monks refer to the Rule as what makes a monk, and talk about people who are careful in their observance of the rule as good monks and good people. They're very practical, so they know that other skills are also important for the abbey, such as having a good business sense or being good at reading people, but they still talk about the Rule as the measure of monasticism.