No. The most common mistake made specifically by atheists is, IMO, encouraging theistic would-be debaters to perceive the matter of whether deities exist as something worth discussing. That serves only to motivate pointless debate with no purpose.
This category mistake you are describing is actually both inacurately described and somewhat more typical of theists than of atheists. It is theistic preachers, not atheists, who often feel the need to convince others of the merits and truth of their deities - thereby taking an attitude that would better fit particularly immature believers of lesser supernatural deities despite nominally being believers of a monotheistic deity of an entirely different level.
Atheists tend not to care one way or another. But they are very much in the wrong when they decide to answer such inane arguments "for the truth of monotheism" in such feeble, pointless terms. It is far better to just decline to lend credibility to what is unworthy of it.
Instead, to the extent that your distinction is both sensible and real (and this is really entirely arbitrary, since we are after all talking about mythology here) it shows the biggest mistake of monotheistic preaching: its very root claim is at odds with its goal. If there is only one "true", transcendental God, then it is pointless and self-contradictory to want to convince others of its existence. He will by necessity be an abstract principle and believing in his existence will be, itself, a mistake of category. Such entities are to be used, described, used for motivationala and inspirational purposes - but never to be misused in claims about whether they exist. They exist exactly to the extent that people want to make them real, no more and no less.
