It is possible some hypocritical motive might make this so in some cases.  But the Confession is clear that it is not the Flesh in every case. At least some number are moved to respond by the working of the Spirit just like those who are regenerated are so moved.

That’s what “common operation” means, common to elect and non-elect alike.

Others, not elected, although they may be called by the ministry of the Word, and may have some common operations of the Spirit, yet they never truly come unto Christ, and therefore cannot be saved