"Partisanship" means bias or prejudice, and "impartial" means neutral or treating all parties equally. Thus, they're antonyms.

The use of "while" hints that we're looking for words that have negative tone,
and means promoting/encouraging/permitting neutrality
or means discouraging/preventing/inhibiting bias.

A. expediting means the tools would make bias happen faster, so it doesn't work
B. constraining means the tools would limit bias, so it's a perfect fit
C. facilitating means the tools would make bias easier or possible, so it doesn't work
D. deterring means the tools would discourage or prevent bias from happening, so it's a perfect fit
E. exacerbating means the tools would make the issue of bias even worse, so it's totally wrong
F. lamenting means the tools would express disappointment or regret over bias, so it doesn't make sense

Constraining & Deterring are both perfect fits in context, and they are also synonymous.