A politically-focused paper may harm your standing among those with an opposing viewpoint. This perhaps should not happen, but it's an unfortunate reality of human nature.
If you publish a paper that could be interpreted as "party X is worse than Y", people (even scientists) are going to read that through a lens of their own biases, to some extent. If they support party X, they may be less likely to believe your conclusions, more likely to challenge you, and/or have an emotional reaction against it. Some people will be able to be impartial and rise above their biases; for others, this may lead to a final judgement about you.
How much this harms you may depend on which side you take. There have been many studies showing that college professors tend to overwhelmingly favor one side of the political debate in America. Here is just one example. This effect is far more extreme in some fields than others.
So, another unfortunate reality is that, depending on the side your paper favors, the results may be very different for your career. You might be confirming the beliefs of 95% of your colleagues, or you might be challenging those beliefs. I hate to say this, because it sounds like a suggestion of "only do this if your finding matches the existing orthodoxy", which is a highly unscientific approach. But I do think this point needs to be acknowledged.
A political paper may get a lot more attention than the average paper. Papers like "adherents of party X pick their nose a lot more than adherents of party Y" make great headlines and often get picked up by the media. They are second only to studies claiming that chocolate, beer, etc. are good for you, in terms of press appeal.
More publicity for you is typically a good thing (assuming you are doing good work). The fact that you published a well-known paper can be a great thing to have on your CV. On the other hand, it does raise the stakes. Your paper would be subject to a lot more scrutiny than normal.
In the end, only you can make this decision; there are risks. But my feeling would be evaluate this very carefully, but do go ahead with it if you think it would make a high quality paper. Some points on how to proceed:
- Don't move forward without someone experienced on board. Make sure you can get some good, respected people's input. Ask them about the general idea before you start, and make sure someone more experienced than you is willing to contribute and be an author if you do go ahead with it.
- Work hard to overcome your own biases. I would try hard to find someone with an opposing political viewpoint to review it, to make sure I'm not missing something obvious because of my own bias. There may be an alternative reading of the data which I haven't seen, because I'm predisposed to think ill of party X.
- Do the work meticulously. If this paper does get attention, any error or methodological issue is likely to get picked up. Make sure you do everything very carefully, document all your methods, test thoroughly, etc. (Of course you should always do this).
- Report the findings in as evenhanded a way as possible. Don't take unnecessary political potshots. Don't assume bad intent where your results don't warrant it. And think about the title you want to give it. Do you want it to say "Party X is more evil than party Y" or something generic like "The relationship between Foo and party affiliation".
- Make sure not to claim too much. Be clear about the limitations of what your work actually shows. It's quite common to see papers that jump to unwarranted conclusions or assume causality where they haven't shown that. Steer clear of such things. Make sure to be clear about your limitations, and if there are multiple possible interpretations of the results, make sure to discuss them all.