(1) The one that stands absolutely no chance of success is trying to persuade Ms. Blue not to like Obama. If she ever comes around to that view, it will have to be with no help from you. Depending on her personality, she could react by doubling down and becoming the last Obamaphile on Earth (other than, of course, Barack Obama), or resenting your efforts as disrespectful of her, or in a worst-case scenario, turning off you.
(2) Similarly, don’t mutter under your breath anything like, “You’re so smart. How could you ever vote for him?” See, women hear things muttered under men’s breath, and we take offense. Just because you say it quietly doesn’t mean it can’t be heard as clearly as if you had used a bullhorn.
(3) And don’t let this difference become fodder for bickering. You knew she was an ObamaGal the minute you first saw her bumper sticker, so you went in with your eyes open. Don’t pick fights over this, as tempting as that will be, or use it as a wedge issue to complain about something else about Ms. Blue you may not like. Keep politics out of your conversations.