I've been running a forum with my spouse since I started it 10 years ago. I should say that we've been together for 14 years, been married since 2010, but overall it hasn't been a problem.
In our relationship, we're best friends first, and the way we act toward each other on the forum, is pretty much the way we are offline, and being the extremely private people we are, we wouldn't post anything on the forum, that we wouldn't say in a room full a people and so, for us, it works.
We avoid this situation by not being in it in the first place.
I have been on forums with nauseating, attention-whoring couples and individuals who have felt the need to mark their territory on each other in topics throughout the forum, that is, if they weren't using other topics on the forum as some sort of foreplay with way too many tmi comments, or posting personal announcements (be it a pregnancy, birth or trying) as though any one on the forum cares. If you are running a family, parenting or pregnancy forum, or a forum with friends and family only, then that is one thing, but outside of that, and it is a blatant attempt at getting attention for yourself.
And god forbid, that you speak up about it, because then you're just jealous, bitter, lonely or never got laid, don't have anyone at home.. etc., and not because their behavior is in any way unprofessional, inappropriate, or alienating to people. If it's one person complaining, then you might have a point, but if it is more than 10, then you have a problem. Which these admins usually solved with a ban.
The only thing more hilarious than couples and individuals like these are the ones who have broken up, and 9/10, it's the same people.. and it is sad because at some point the community did get attached to one or both of them and people will eventually take sides, that's if it didn't immediately kill the community, which, over time, it usually does.
As for the other 1/10, the couple listened to what people had to say, apologized for their behavior and decided from then on to keep their personal stuff off the forum.
I have always said, that if you have to post about how special your relationship or life is, and constantly lay it on thick and mark your territory where your partner is concerned, then your relationship or life isn't really special to begin with your days together are numbered.
I've heard that a few years ago, a major forum host went under as a result of a divorce, when the owner could no longer afford to keep the service up. So if anything, that's probably a good reason not to have your spouse or s/o involved, but it can work if you are just running a forum, you just have to watch your behavior on the forum in the same way you would watch what you'd say if you were in a room full of people..