Is a Muslim obligated to leave his job at a restaurant free of alcohol, but full of temptations, music, and intermingling with immodestly dressed women, along with mockery from the workers, fearing a loss of livelihood?

If the establishment includes abominations such as disbelief and mockery of religion, and you are unable to denounce them, and you have what suffices your needs until you find an alternative job, then you must leave it to preserve your religion. For whoever gives up something for the sake of Allah, Allah will compensate him with something better. Allah Almighty said: "And He has already sent down to you in the Book that when you hear the verses of Allah being denied and ridiculed, do not sit with them until they enter into another conversation. Indeed, you would then be like them. Indeed, Allah will gather the hypocrites and disbelievers in Hell all together" (An-Nisa: 140). However, if you are able to denounce the abomination and are safe from temptation, or if leaving the job will lead to ruin, then do not rush to leave it until you find an alternative.