Kicky, the answer to the question is, no, they can not. It's actually another temple interview question.
6. Do you affiliate with any group or individual whose teachings or practices are contrary to or oppose those accepted by The Church of Jesus Christ of Latter-day Saints, or do you sympathize with the precepts of any such group or individual?
Wow, I've never interpreted that as a political question. I've always understood it to mean, "Do you support any anti-Mormon groups?" Otherwise both active Democrats and Republicans would have to answer "Yes" to the question, because (to my view anyway), there are plenty of teachings and practices in both parties which are contrary to LDS gospel principles.