Is it permissible to work in a gambling café – while limiting oneself to serving only permissible (halal) drinks – when there is no other source of livelihood?

It is not permissible to engage in any work that involves assisting in what is unlawful, except out of necessity; this is based on the Almighty’s saying: "And do not cooperate in sin and aggression." There is no objection to your brother working in a place that serves permissible drinks as long as it does not involve assisting in what is unlawful. However, the concern lies in his witnessing evil without condemning it or leaving the place. He is not permitted to do so except out of dire need, while necessarily condemning it in his heart. If he finds permissible work that is not surrounded by evil, he must move to it.