Who would dispute the separation of powers and why?

The highly religious, American Christian Churches.

Explanation:

if you mean when the separation was put in place then Puritans would have definitely opposed it.

other opposing groups would be Catholics (Vatican controlled by the Pope), Muslims (Sharia or religious law), and evangelicals who currently hold some sway in politics today

Separation of powers is a political doctrine originating in the writings of Charles de Secondat, Baron de Montesquieu in the Spirit of the Laws, in which he argued for a constitutional government with three speedways branches.