Let's say you are a high-power lobbyist in Washington. You've spent decades cultivating contacts, making deals, basically working up your way till you are in a position to lobby at the very highest levels of government on behalf of your clients. You want to have a meeting with the vice president. Or perhaps you're a representative in congress, and wish to discuss issues pertaining to your district with the VP. Sound like regular business on The Hill, right? If you happen to be a woman, you will not be able to have a meeting alone with the US Vice President Mike Pence.
According to a profile of his wife Karen in the Washington Post, Pence will not dine alone with a woman if his wife isn't present, nor will he attend an event that serves alcohol if she isn't there.
Of course, there's nothing necessarily wrong with this stance, and as the article shows, he does this with his wife's approval. However, it does mean that there are professional settings that he will not avail himself to, if the other party is a woman.
Of course, this stance is in keeping with his other... old-fashioned positions on women, such as the belief that they don't have the right to decide what they can or cannot do with their own bodies. As governor of Indiana, he passed an extreme law that all but banned abortion in the state. He also passed a similarly draconian "religious freedom" law that basically permitted open discrimination against LGBT people.
Oh, and he also holds meetings about gutting maternity care provisions in Obamacare — without a single woman present.