Is it permissible to work for a company whose owners are predominantly, or very likely, innovators (Ahl al-Bid'ah), knowing that the work environment is mixed and includes employees from among Ahl al-Sunnah?

If the exchange company adheres to the Shariah-compliant conditions for currency exchange and transfer, then the fact that its owners are people of innovation (Ahl al-Bid'ah) does not preclude working for it, unless working with them leads to religious tribulation (fitnah), such as unlawful mixing or promotion of innovations. As for the first job, its ruling depends on what was agreed upon between you and the company regarding rights and obligations.