Can a believer be used by Satan to accomplish his purpose?

Can Satan use a believer to accomplish his purposes? Absolutely. Believers can get sucked into ideas and beliefs, whether specific causes, political beliefs, thought patterns, or other ideas, that are demonic in nature. The apostle Paul even warns about this in 2 Timothy chapter 2. This is why knowing God's Word and being able to discern His voice is critical, especially in an era where there is so much deception.