Well, I think it's different strokes for different folks. I don't see so much a right or wrong way with taking either stance, each person and each couple will have their preferences and tolerances and that's ok. But honestly, I find the "staying in touch" camp to be far more rife with potential complications and problems.
My personal take on it is if you meet a great person, a great match, that's not that easy in life and there are already so many other hurdles and complications to getting a relationship to work before you even get to the issue of an ex spouse or ex relationship, that why would you want to stack one more problem or one more potential roadblock in your way when you don't have to do so?
I think if you get to a point in your life where you are in a relationship with someone who has a child from a previous relationship, that you are simply buying into dealing with more as part of buying into the relationship. You simply can't railroad out half of a parenting duo if that person is trying to actually be a decent and functional parent. I suspect this issue is one of many reasons why so many single mothers are seen as undesirable for dating/relationships/potential marriage.
Personally, I wouldn't be ok with it. I think this is just one of those issues where if you have widely differing values from the other person, nothing good will come of it and will likely be a deal breaker. ( i.e. like issues of marriage, having kids or not, religion, views on money, etc)
On a more ruthless note, from strictly a male perspective, based on observation over time, is that as a guy, you have to accept that just because a woman is married or engaged or has a kid with someone or has a family doesn't mean she loves the guy, doesn't mean she even wants to be there, doesn't mean she isn't waiting for her first chance to jump ship. I see lots of women hook up, get into relationships and get married and have kids for all kinds of reason that have nothing to do with love. Some are just lonely. Some don't want to be the last of their friends to have a relationship or marriage or kids. Some are bored. Some feel social pressure. Some just transition their college relationship into a marriage. My view is the more you have to offer as a male and the more she values you, in general, the more she will not want to add to the number of roadblocks to get you together and/or to keep you around. If you are Derek Jeter or Tom Brady or Chris Hemsworth or George Clooney, do you think most chicks would put up a huge fight about keeping a Facebook conversation with some guy she used to bang two years ago? However, the less you have to offer her, the less esteem you hold in her eyes, if you are just a guy who is good enough for right now to buy her dinner and tell her she's pretty and make sure she's not lonely on holidays, then she might care less how you feel about her Twitter or Facebook dealings.
In truth, what I see around the world, observing people, taking stock of thing around me, that most people I notice hang around their exes because their exes offer some value to them. Some people like to dangle an ex because they know the person still holds a little bit of a torch for them, and it makes them feel good to have that point of validation when they want or need it. Sometimes you are just a useful person to them. Maybe you are a mechanic or a lawyer or your uncle is an executive at a big corporation or your cousin runs the hottest club or bar in the city or your aunt can get tickets to the best shows or premieres or reservations at the swankiest restaurants.
As for the "trust" issue, I'd be pretty leery of anyone who wants to box you into a lose/lose situation. There are just some truly worthless POS jerk offs out there, men and/or women, who will openly flirt with an ex or just other people, in front of their relationship or spouse, even in front of others like friends and coworkers, and then fall back onto the "trust" defense. "Why don't you trust me?" You say nothing, they disrespect your relationship. You say something, and then you are labeled as whatever they want to call you in negative terms. I think each person has to define for themselves as to what they see as "respectful" in a relationship and hold to those values. I don't believe you can love someone without respecting them first, so if you feel you aren't being respected in a manner in which you would want to treat yourself and others, then it's probably time to walk and punch the eject button.
In terms of dealing with the opposite sex, I wouldn't generally trust a woman who has ZERO female "friends" and is surrounded only by male "friends". I think it's a red flag. Don't get me wrong, it's probably tough for most women to find a loyal core group like the Sex And The City girls, but to have ZERO female friends as a chick would indicate some deeper flaw IMHO.
On the flip side, I wouldn't trust a straight guy who is always surrounded only by women and has tons of "women" friends. ( My take is that most women, aside from some specific work/social circumstances, can barely stand each other. Most IMHO simply hate each other. Often many are competitive and catty and vicious to each other deep down. Any guy who can deal well with so many of them at once, isn't a guy I'd trust to watch my back.)