Let the Lord worry about it is, I expect, more of a reference to the practicality of not causing waves for the sake of the Gospel. Earth governments wax and wane and will all perish, but the Kingdom of God has never stopped growing.

God can grant you freedom within tyranny with more ease than you can grant yourself freedom in the wilderness. The act of paying taxes and disregarding government by just checking the boxes is a practicality for getting the least amount of attention while you strive after eternal goals.