Should I choose a university where technical ability and social responsibility are both taken seriously?

Yes. A university that takes both technical competence and social responsibility seriously can be a strong choice. However, it should not be your only criterion. Check the content of your intended field, how ethics and social impacts are addressed in laboratories, practical classes, or projects, the academic support available, and whether the learning environment suits you. Practices differ by university, faculty, and program, so use official information and open days or other opportunities to verify the details.