I think the idea of the power of persuasion is both important and a useful tool. It is worthwhile to persuade a person that your position is the right one. I believe that expressing strong convictions and presenting and defending your point of view is very important in the process of persuading a person to switch from their original position over to agreeing with your point of view.
I think that a person who pretends to be sympathetic with the opponent's position with the purpose to persuade someone to come over to their side leaves himself or herself in a vulnerable position. Plus, the person who you are trying to persuade may hold firm to his or her belief, and may be able to tell that you are wishy-washy on the issue and might try to take advantage of that. Moreover, what if your wishy-washiness is detected as a con, an attempt at manipulation, and you lose credibility?
The more you weaken into a "center" position, or pretending to be a friend of the opposite point of view instead of holding true to your convictions, the more you leave yourself open to the other side's position slowly seeping into your consciousness and then actually converting you over their side, or agreeing with their position.
I believe the only chance a person has of persuading an opposing person to change his or her mind is to hold true to one's point of view firmly and with conviction.