One of our coaching clients has been fortunate to do work for some very well known people. We discussed using that information when he promotes his business.
He said, laughing, that he has to be very careful what he says and to whom. He does promote the fact that all his employees have been checked out by the FBI because they work on highly secured buildings and homes. But not everyone looks on the former President with favor – in some circles, he'll gain business because of the connection, in other circles it can cost him the sale. So he namedrops only if it he is sure that the person he is speaking with is a died-in-the-wool member of that political party.
He follows the rules of polite conversation that our mothers taught us (and not too many people follow anymore) – the three topics you avoid are s**, politics and religion.
He also doesn't let someone else's political views prevent him from working for them. As he said, "If I refused to work for people because they are a democrat or republican, my checkbook would be about half of what it is today." Refusing to work for someone because they have a different point of view does little more than hurt your ability to take care of your family.
Stay cool and stay informed. Always listen politely and keep your opinions to yourself. Until you get in the voters booth. That's when you let your opinions fly.