Please keep in mind that your question is not really an apologetics question, so all that I can offer is my personal opinion.
That said, I think that all of the notations you mention indicate a serious breakdown in social civility and hospitality. Basic civility requires answering a social invitation without prodding by the hosts. Hosts may have little choice these days if they are hosting a large event for which they need an accurate count, but the RSVP notation (and even more so the RSVP card) were an unfortunate concession to bad manners by guests. Printing registry information on an invitation, on the other hand, has always been and we must hope always will be a hideous display of greed by the couple. Registries exist so that those guests who cannot think of a present to give may ask the couple where they are registered and then look up a list of gift suggestions. Unfortunately, these days, too many people think they are a list of demands that must be fulfilled by those sent an invitation whether they attend the wedding or not.
Moving on to your concern, a notation of “Adults only” on a wedding invitation is both a concession to bad manners and an unfortunate attitude by couples preferring aesthetic perfection on their wedding day above the presence of child family members. It is a concession to bad manners because polite people should know that they cannot bring to an event anyone who has not been invited, but they persist in asking their hosts if they can bring dates or children (or, more seriously, show up with extras in tow). Such a notation lets the guests know that the hosts don’t want children present. But not wanting children present, as you have perceived, is a poor attitude for an occasion on which a new family will be created that is supposed to be open to the possibility of new life.
It should go without saying though that a guest who has children who have not been invited should either find a babysitter and attend or politely decline the invitation without volunteering why he or she is unable to attend.
