Publishing as sole author on politically charged topic
I want to begin by acknowledging that I am stepping far outside my core expertise by answering this question: as a mathematician, the chance that I would write an academic paper on a politically charged topic is essentially zero.

I firmly believe that PhD students have the right to work on whatever they want in addition to their assigned thesis work and duties.  (In fact, everyone does.)  When I read other questions on this site in which students in the laboratory sciences say that their advisor tries to shut down their side interest in X, I got dismayed.

Being a PhD student requires a great deal of single-mindedness.  I think it's nice for a PhD student to have at least one project or publication which is not directly connected to the subject of their thesis work: that shows breadth.  However, this should not come at the expense of their thesis work.  Sometimes people with very independent personalities put more time into their independent work than their guided work, and this can be a good decision, but they should still get guidance on that decision!

In this case, I am a bit concerned that the OP may be going out too far on her own.  This is a side project which has some difficulties -- including political ones -- to the extent that the OP is wondering whether she needs more faculty assistance.  She also says that she has not published anything previously.  So the OP has chosen in my opinion a rather tough side project.  How much effort will it take to bring this project to successful completion (including publication)?  The OP doesn't know; that's part of the question.  

I recommend that the OP talk to her advisor about this project, including the question of how much time to spend on it and whether to try to publish it now, later or never.  If the paper is sufficiently politically charged, then it has an unusual property among academic papers: publishing it may damage the OP's reputation in certain circles.  This is already worth a serious conversation with the advisor.  

Finally: adding coauthors solely to increase the chance publication is both unethical and a suboptimal strategy for the solo author.  I have a different idea: if the paper is hard to publish because the author is so junior, the author can just put the paper in her pocket until she is less junior, and then try to publish it later.  (There is also something to be said for not having your first publication be controversial, at least in many academic fields.)  What a PhD student needs to do most of all is complete the strongest possible PhD thesis, and this strategy ensures that the OP is not getting derailed from that.