Working in an internet café where they allow movies and music

Listening to songs and music and watching movies in which men and women mix and in which ‘awrahs are uncovered, and which are accompanied by music, are all haraam things. It is not permissible for the owner of the café or those who work there to allow anyone to do these things or help him to do that. This has been discussed in the answer to question no. 47396. 

Based on this, if you can prevent people watching movies or listening to music, there is nothing wrong with you working in that place, otherwise you should leave that job, seeking the pleasure of your Lord, and so as to avoid approving of evil and keeping quiet about it, which would incur the wrath and anger of Allaah, may He be exalted, as Allaah says (interpretation of the meaning): 

“Those among the Children of Israel who disbelieved were cursed by the tongue of Dawood (David) and ‘Eesa (Jesus), son of Maryam (Mary). That was because they disobeyed (Allaah and the Messengers) and were ever transgressing beyond bounds.

79. They used not to forbid one another from Al-Munkar (wrong, evildoing, sins, polytheism, disbelief) which they committed. Vile indeed was what they used to do”

[al-Maa’idah 5:78, 79]

We ask Allaah to help us and guide us. 

And Allaah knows best.