For laypeople, cultivating renunciation also means not to be covetous of worldly things. Non-Buddhists cultivate renunciation as well. Many non-Buddhist monks or clergies do not wish to remain in samsara. They too seek liberation. However, lacking the right view, theirs are not considered true renunciation.
Excerpt from the Luminous Wisdom Book Series ~ "The Right View : The Three Differences."