Is it permissible for a sports club to train boys and girls in karate in private clubs affiliated with non-Islamic municipalities, knowing that this is their sole means of livelihood, and if they do not agree, other trainers will be brought in?

There is no objection to learning or teaching karate for men and women, provided that Sharia (definition) compliance is observed, such as avoiding free mixing, adhering to the-Sharia-compliant dress code, observing prayer times, and avoiding striking the face. Therefore, it is not permissible for the questioner to work as a coach unless these controls are met, and his argument is not a justification for remaining in a forbidden occupation.