Indeed it should, but then we're not fighting Planned Parenthood as such but principalities and powers. Scott Hahn writes in his latest newsletter:
It's important we take part in the [political] conversation. And it's good for us to be passionate. But we also need to keep perspective. Those of us who have survived a few disappointing elections know that God can draw much good even from the worst outcomes. A sense of history can be helpful.
Still more than history we should turn to Scripture. St. Paul had no trouble speaking out against the evils of Greco-Roman culture, but he knew that the real war was more than cultural. "For we are contending against not flesh and blood, but against principalities, against the powers, against the world rulers of this present darkness, against the spiritual hosts of wickedness in the heavenly places" (Eph 6:12). The real battle requires spiritual combat.