In this world of "drama" that we surround ourselves in to make a living, we have to remember that it is still work and that it is still just a job. This is simply an unhealthy office romance. People will look at them strange, there will be a weird feel in the air, but they're actors, they're job is to perform onstage the characters that they and the director set during rehearsals. If the romance goes sour, chances are it won't affect the show, because she needs that employment just as much as anyone else---plus it's her (and his) professional reputation on the line.
At worst, they'll be cold to each other backstage and the romance scene will be awkward for a day or two. If it continues to affect their performances, then you step in and say "I think we've lost some of the motivation in scene XX" or something like that.
You keep focused on maintaining the show. Let them maintain their personal lives.
Short story that reminds me of this: I had two guys a few years ago in a show who were getting romantic backstage (they were playing father and son in the show) and for about 5 days in a row, when I called 15, they'd still be chatting up a storm and not in costume or makeup. The same would be true when I called 5 and then they'd rush off to get ready. But really, my job isn't to demand how they spend their half hour, only to make sure they're ready when the curtain rises! So on the fifth day, I said "guys, chat all you want to, but at 8:00 the show starts, and I'm not holding the show for you if you're not in costume and makeup." It got the message across. They knew that they were there to do a job and it fixed the problem.