The immediate solution to this (assuming the feature stays) seems to be a stricter sign-up / verification process that ties your account closer to your real-world identity before you can use political features like this, to make bots and fake accounts more difficult to create and/or influence politics through these direct lines.
Tinfoil hat:
Fortunately (or unfortunately), that's also a step closer towards (but not at, yet) the verification necessary to start, I don't know, actually voting through Facebook. I wonder if giving bots a direct line to local politics would actually result in people/lawmakers _begging_ more verifiability to Facebook accounts, instead of Facebook trying to implement such a process/feature without the inevitable backlash they'd no doubt get if they said "you can now link your social security number to Facebook!". Being verified as a real human on Facebook ultimately helps Facebook get closer to a potential goal of giving petitions (or votes) on Facebook more weight.