On a failed attempt to reject such a shift, you take one condition for the failed rejection.
The GM chooses to either give you a second condition from the Label shift that can't happen, or apply a different shift to your Labels.
According to the explanation of the reject someone's influence move,
On a miss, your Labels most likely shift in exactly the way you tried to resist[.]
That "most likely" makes clear that this is a suggestion, not a hard rule - the move text itself says "the GM adjusts your Labels" but doesn't specify it has to be in line with the original shift.
In the case where this shift would cause a condition, the GM is perfectly within their rights to give you one condition from the missed reject, but choose a different Label shift that still relates to the situation in play. In this case, you'll only take a total of one condition; the original Label shift doesn't happen, replaced by the other shift the GM applied.
Following the example from the book for taking a condition from a disallowed Label shift, consider Huma, the Legacy, being told "he's a great hero, the saviour the city needs". This triggers a Label shift increasing his Savior and reducing Mundane, but his Savior is already +3.
If he accepts the influence, his Savior can't shift up, so he takes a condition instead and his Labels don't change.
If he rejects the influence and rolls a hit, his Labels don't shift and he gets the usual benefits of a successful reject someone's influence.
If he rejects this influence and rolls a miss, he takes one condition and the GM adjusts his Labels once. The GM could decide that Huma marks Insecure, and feels pressured to perform perfectly, better than everyone else, shifting down his Mundane but increasing Superior instead of Savior.
The GM could instead decide to shift Huma's Savior up and Mundane down as originally planned; in this case Huma takes one condition from the failed attempt to reject someone's influence, and a second condition as his Savior could not be increased; he takes two conditions, but his Labels don't change at all.