Couldn't have been more wrong vs Couldn't be more wrong

The only difference I see is past tense versus current tense: WAS wrong versus AM wrong. It is an extremely minor difference and probably irrelevant in most cases. Although, personally, as the example sentence is past tense, I would use 'couldn't have been", also past tense.

A grammarian might have a different view?

If you couldn't be more wrong, why don't you change your opinion, so that you were wrong but no longer are?

On the other hand, that jerk of a neighbor of yours was wrong and still is. In fact, he couldn't be more wrong, but he refuses to change.