There is a job search in my department. The department is extremely divided on the candidates. As new faculty, should I abstain from voting? Is this a prudent choice?
It could be. It could also be a disastrous move. There is no way an outsider can judge just how messy your department is. Your best bet is to find someone in your department that you trust and ask them. I personally think jut abstaining for a hiring vote is a little weird. If you go down the abstain route, you may be best off abstaining from all votes.
The STFU strategy can work, but in really divided departments, at some point before tenure review you are going to have to take sides.
I suppose to some extent, this depends on how new you are. You were invited in to the department to participate as a faculty member, and that has to start eventually.
I suppose it also has to do with whether you understand the issues surrounding why the department isn't coalescing on a single candidate. If the reasons concern long-standing departmental issues that you don't have a grip on yet, you might choose to listen, to bring yourself up to speed, instead of talking.
If you feel that you are in a position to have a UNIQUE VIEW that the rest of your faculty can't have -- like maybe you're the only faculty member in the same professional organization as one of the candidates, and every time the candidate gets up to speak in front of colleagues, the attendees start laughing uncontrollably because the ideas advanced are so silly (this is, of course, an absurd case, before the downvotes roll in). If this is the case, you have insight that your faculty doesn't share, and you owe it to them to chime in.
If you don't have any strong views, and think you can work equally well with either candidate, you might say so, then sit back and watch how things work out.
Another tack you can take is to not go public, but just send an informal note to your chair summarizing your views, or just a note saying what professional interactions you envision personally for each candidate, without endorsing either, to give the boss some more info to be used for a decision. Of course, you can't assume that your email won't be shared. You could also just have a conversation with your chair.
Lastly, consider the environment surrounding the recruitment. You're a new hire, and your department is making another new hire. Your department is expanding. Is the cluster of hires intended to create strength and depth in an area of research in which you are involved?? If so, I think you need to chime in, as this new recruit is being brought in as your colleague, and your opinion may be central for consideration.
It all depends on WHY they're divided. If it's about the overall direction of the department, then that suggests a different course than if they're divided on the candidates' qualifications and body of work.
There's no real way to give a concrete answer. Is the dispute pedagogical? Ideological? Personal? Affirmative-action-y? Is it old-guard vs. young-lions? Is your future tenure committee firmly on one particular side?
Bear in mind, in candidate searches it's also valid to vote "none of the above."
Every open expression of opinion, can be considered an "investment of reputation". That investment can pay off, or it can be lost. Reputation can be invested purely for political reasons (e.g. to increase your own, which however may be considered questionable), or to improve a faculty-level decision in a strategic way which you consider favourable to you. As a new faculty, you probably do not have a lot of reputation points yet, so you should be sure that you invest wisely.
So the importance of the decision and the quality of the investment should be balanced with your information about the case (departmental strategy, candidate, etc.) whether this is an investment you intend to make. If you do not have enough information, as in a business investment, staying away from it is a perfectly reasonable decision. Just work on acquiring more information for the future.
Note that, also, if you are a very new faculty, some departments may regard that as premature for you to join in with hiring decisions - you would have to find out whether this is the case; as a plausible rule, if this hire takes place essentially in the same "batch" of hires in which you were brought on board, it probably would be good form to not interfere with the hires.
[Note: The OP's original question is extremely vague, so let me clarify that I'm answering the question as it was interpreted by later editors]
In my opinion a key question here is whether the vote on the search is done by a secret ballot. The goal of secret ballots, in faculty votes and more generally, is to allow people to vote their conscience. If the ballot is secret, then I would advise you to vote for whatever option seems to you to be preferable for the future of the department, and not to be influenced by any political considerations. If you are genuinely unable to decide which option is better, due to being new at the department or for any other reason, then you should abstain -- this is precisely what abstentions are for.
If the ballot is not secret, then it should be. Faculty votes on sensitive decisions pertaining to hiring and promotions should always be confidential and anonymous, precisely to allow people to express their honest opinions without fear of repercussions, and to prevent well-known negative phenomena such as groupthink and factionism. What I suggest in that case is to go to your department chair and express concern that you are unable to vote according to your true opinion without fear of being seen as taking sides in a politicized, divided debate, which is untenable given your status in the department. Tell the chair that therefore you will be abstaining unless the vote is held as a secret ballot, and ask for the chair's help in ensuring that the abstention is understood by other faculty members and does not antagonize any of the factions.
I think this approach minimizes the risk of offending people, although it may not completely eliminate it. Furthermore, although I am incredulous that some departments even hold non-secret ballots on hiring decisions, I have a feeling that in some places where this happens there may be a policy that says the ballot can be made secret if this is asked for by one or more faculty. In that case, going to the chair can actually make a difference in ensuring that the vote is held as a secret ballot, thereby resolving your dilemma.