Why is the distance between the atoms shorter in the dicarbon anion compared to the cation?
Looking up in a current compilation of bond lengths in the International Tables for Crystallography (IT), apparently there is indeed not so much deviation in the distance between two adjacent carbon atoms in a $\ce{C(sp)#C(sp)}$ pattern:



(IT, 2006 edition)

Some hints to render this excerpt easier to access.  The IT indeed discern different bond types (13 for all combinations of $\ce{C-C}$,  and 625 for all organic / organometallic compounds), and consequently, the source offers separate listings for, for example, $\ce{C(sp^3)-C(sp^2)}$ or $\ce{C(sp^2)-C_{ar}}$, too (first column). The second column is about the structure around the pattern in question highlighted in bold. For the $IT$, $\ce{C_{ar}}$ explicitly represents an aryl C in an six-membered ring; $\ce{C^{\#}}$ any $\ce{C(sp^3)}$ - linearly substituted, or not.

The third, fourth and fifth column are the unweighted sample mean $d$ in [Å], sample median $m$, and sample standard deviation $\sigma$, followed by the lower and upper quartile, $q_l$ and $q_u$, as well as the number of observations $n$.  Overall, the compilation is based on a subset of 10&nbsp;324 X-ray and neutron diffraction data found in the Cambridge Crystal Database by September 1985, judged to be "good enough" (the source offers additional insight about the criteria applied).