It certainly creates conflicts of interest with the goal of an election, or rather a mixed group decreases the motivations for collusion

>"Does political affiliation affect integrity somehow?"

I'd say so, but not in a sense that the effect is only or even primarily associated with [insert political party here].

Edit: We like to envision Judges as impeccably impartial, but they have a considerable amount of leeway, ambiguity, and procedural caveats they can employ should they choose to make partisan decisions. Given that judges are often selected by, or elected with support from, a political party machine, it stands to reason that they can be swayed to help the party that is responsible for their position. Especially if there is plausible deniability of bias or wrongdoing.

If you need all the members to sign off,

And a member of party X is more likely to be willing to cheat to benefit party X,

Then having all the members that need to sign off be from party X does indeed increase the ability to cheat for party X.

I'm not sure how it works in Philadelphia, but in Chicagoland the EJs don't generally know each other; we meet for the first time the night before the election to set up the polling station. If you floated the (insane) idea of trying to rig a precinct, the likelihood of one of the other EJs reporting you is extraordinarily high. Meanwhile: the likelihood of you being able to flip even a township election by doing this is low. It just doesn't add up.

I think you have to have some pretty huge procedural gaps to make this viable, which is my point here.