During the Paleolithic era, hunter-gatherer groups began to develop cultural traits. What was the most important influence on which cultural traits developed?

This would be language. Language is one of the first ways how culture was being spread and our hunter-gatherer forefathers started differentiating from each other. As a tool, language is obviously extremely important and for that reason it also had the most impact on daily life and influenced other cultural traits through it that were developed later as well.