Spiritual or Secular?

Can a Christian separate their spiritual and secular lives?

Yes (he can at least try).

Should they?

No.

The Israelites weren't content with Samuel as their spiritual guide and God as their king and petitioned Samuel to have God appoint a human king. God, through Samuel, warned them that the king would
  • take their sons and put them into battle
  • take a portion of their land
  • take part of their earnings
They forgot that God himself had won their military victories, brought them prosperity, and created their nation. He was active on the battlefield as he was in the worship service. - Henry and Richard Blackaby in "Spiritual Leadership."

Yes, we can try to separate our lives from the spiritual, but we were made spiritual human beings. Even the non-believer is spiritual. Every one of us have spiritual needs.

To not apply the spiritual in all our lives is a divine problem. Christ is the believer's Lord; in all areas, at all times. God does not intend there to be a distinction between work and worship....it's the even the same Hebrew word.

For the eyes of Lord range throughout the earth to strengthen
those whose hearts are fully committed to him. - 2 Chronicles 16:9a