To be a participant in something, for example, football. A person would be a member of the team and would actively practice and play with the team. If we participated with demons, then that would mean that we were on their team. Since we cannot serve two masters, or play for two teams, because only one would get our best or both would suffer with half-hearted committment to the team. God is a jealous god, and will not tolerate our being half-hearted, luke-warm, in Revelation, He says He will spit them out.
The church was still used to a polytheistic society, new believers from the cults tried to bring their favorite rites to the church. But these rites identified them as belonging to the cult, not as a Jesus follower. Paul wanted the new believers to be easily identified as belonging to Jesus. This helps new believers to leave the old life behind.