political football
an issue presented by one party or the other that is not a political issue at all, yet is tossed around by politicians to gain sway or distract voters from the REAL issues. Abortion, DACA, and gay rights to name a few.
Republicans throw around their abortion argument like a political football to prevent real discourse on reproductive rights for women. Democrats toss around this political football in their own right, resulting in neither talking about reproductive rights in general, but rather a personal religious belief.