From Guy Duinincks.

Touch Not God's Anointed
Some ministers use the words, “Touch not God’s anointed,” to insulate themselves from scrutiny or criticism. The implication of their words is that since God called and anointed them, anyone who disagrees with them or passes any judgement on them has trespassed onto some kind of “holy ground”where they are not permitted to go. These words, and words like them, are employed to keep believers from examining a minister's teaching and every disagreeing with his leadership. They are often a kind of,“How Dare You!” challenge thrown at believers to keep them in line.
Let’s think about where these words come from and determine if they are legitimate words for any New Testament minister to use for their own insulation or defense. These words come from the book of Psalms. We read:
"When they went from one nation to another, from one kingdom to another people; He suffered no man to do them wrong: yea, he reproved kings for their sakes; Saying, Touch not mine anointed, anddo my prophets no harm." Psalms 105:13-15
In this Psalm, the psalmist had been reminding God’s people of all the ways God had protected them over the years. With these specific words, the psalmist recountedhow God had warned foreign nations to keep their hands off His people and not harm His prophets.
The "anointed" in this scripture referred to all the covenant people of God; to the whole Jewish nation. The warning was directed toward the non-covenant nations and was a warning that they should not to touch His anointed; not harm His people. The “anointed” in this scripture, then, are not New Testament ministers. And the warning given to, “touch not mine anointed,” is not directed to Christians concerning examiningand testing ministers.
It is unfortunate for the church in many places that some ministers have shamelesslyabused this scripture, completely mishandling the Word of God, just to insulate themselves from examination or criticism. Equally unfortunate is that many believers are woefully ignorant of this scripture and what it really means and, being ignorant, have abdicated their responsibility to judge.
The New Testament does not teach that believers are not permitted to test doctrine and examine spiritual leaders. Rather, the New Testament warns believers of the dangers of unsound doctrine and unsound leadership and exhorts them to examine andjudge.
“Touch not God’s anointed” has nothing to do with believers being forbidden to examine ministers.