“Do we have to vote to stop goyim from performing abortions or not?”
In fact, we probably have to NOT vote that way, because we need to have abortions available in the somewhat rare instances where they are halachically mandated for us.
It is a machloket whether we need to vote to force goyim to enact laws consistent with the Noachide commandments. The minhag seems to indicate that the answer is no.