I feel like unless you're on the board for, like, a far-right white supremacist party or something really out there like the Rhinoceros Party, I doubt they'd hold it against you. If it's one of the big four (Conservative, Liberal, NDP, Green), I really don't think they'd care. If you're still unsure or not comfortable, though, you can always leave out the party name.
Just as a heads up, though, when you submit your OLSAS sketch you also need to submit the names of people who can verify your involvement in the role. They only contact these people if they suspect something's fishy with what you've said, but if on the off chance they do reach out (and it really isn't that often, one of mine said that they've been listed as a verifier for tons of law school applicants and schools have never once called), they'll be able to find out the party name then, so it may not even matter.
I can't see a problem mentioning it in law school applications. However, I can't seeing it being more of an advantage than any other EC or community participation during undergrad.
As for job interviews, it's unlikely to be of much benefit and, in some circumstances, may be a detriment.
Accepted this morning! 😄
Still waiting to hear back from Carleton about my admission to the MA/JD dual degree program.
Probably will accept, but not 100% sure yet. Good luck to everybody else!