That's an interesting question. My answer is, yes, you can be blackpilled and at the same time identify with a political idea.
First reason is, politics is how you implement change. If you're complaining about your everyday life and not even bothering to vote, for example, meaning you're not having a voice in trying to change things in your country and consequently in your life, then you do not have the right to complain. Politics is intertwined in every aspect of life, and I do not think it makes sense for a blackpilled or anyone who wants change to be neutral.
Second reason is, there is nothing that puts blackpill and politics at odds. On the contrary, considering that blackpill is an incel ideology, the only logical conclusion for the blackpilled is to support the political side that is anti-feminist. Yes, as you said, incels might not have a voice on either political side, but feminists have a fairly strong voice on one side, and they are not widely accepted on the other side. Here, we can even utilize the weakness of feminism, which is that they are extremely antagonistic toward women who are traditionalist/conservative etc..., and this causes those women to shy away from feminism and instead they focus on issues which is in conflict with feminism which include men's rights. If you think like this, I think being neutral is the more stupid decision. Just my opinion though.
