The contradiction comes from the falsehood of classical mechanics.

First of all, the electrical repulsion exists in both frames of reference, but in the frame that is not moving with the electrons, there is also a magnetic attraction (less than the electrical repulsion). So there is a net repulsive force between the electrons in both frames of reference, it is just less in the frame moving with the electrons.

So if you were to consider the amount of time it takes for the electrons to move a certain distance apart due to the repulsion, you would get two different values.

It turns out these values are related by the time dilation property in special relativity. Maxwell's equation are not invariant under Galilean transformations, they are invariant under Lorentz transformations (google it). This makes classical electromagnetism incompatible with the rest of classical mechanics. This incompatibility played a role in the discovery of special relativity.

So there is no contradiction, you're just using the wrong physics.