I think it's really inappropriate on the adults' part to try to have a "serious" conversation, in which someone's feelings will be hurt by an interruption, when there are children present. It should be scheduled at a time when both parties can reasonably expect to give full attention to each other. Anytime my children are with me, that is not a reasonable expectation, because they have needs too - physical AND emotional.
I do correct my children for interrupting, telling what they can do instead or suggesting something they can be engaged in separately, but for heavens sake, what does someone expect me to do if they continue, lock them in another room? They are clearly trying to communicate something and my job, as the parent, is to pay attention to that and determine what it is they are really trying to tell me by their behavior.
When my friends and I are chatting with children around and we get to something "intense", we joke "Oh, we need to go for coffee!". It's understood that now is not the time. And if you're just gabbing about something inconsequential, then it seems pretty petty to be put out by a child acting like a child.
To each their own, and my kids are "older" (14, 10, and 9 years old today!!!), so I get that babies and toddlers are different, but after the age of 3, I am not going to "schedule" a time to chit chat with a friend that needs me because my child's emotional needs might not be met immediately. I feel that after 40 years and coming up on 15 years of being a parent, I have earned the right to have any kind of conversation I want, with whomever I want, at any time I want, and my kids can deal with it. (and before accusing me of being a neglectful parent, be assured that my kids are very well taken care of and attended to. I am a coach for my DD's cheer team, her troop's Girl Scout Leader, room parent for all three various years, and attend every game and practice my boys have had since they were toddlers in all of their sports, plus never getting a babysitter when they were little or having "me" time even to this day, we eat together as a family every night, and I never let my office schedule interfere with my family schedule).
A "child acting like a child" in this case is an excuse for a parent to let their kid run the show and get their way. At least, it would be in my family. In my family, "a child acting like a child" means that when I say hang on a few minutes and don't interrupt an adult talking, they stop and find something else to do while I am busy. Or, even if we have blips along the way, at the very least, they all understand my expectations of their behavior. We don't excuse it - ever. Even if they are sick, tired, or hungry - once we are alone: "I understand you are tired/sick/hungry, but I was talking to an adult and you were interrupting. It is never OK to interrupt unless someone is hurt or bleeding". That's if I'm in a good mood. if it was irritating enough to put me in a bad mood, my reaction will be more along the lines of "Do that again, and you will be grounded for a week. Got it?"
Since I have done this since they were old enough to understand (aka, age 2), I don't have problems with my kids interrupting after I tell them once, so I guess my suggestion to the question you posed is that I would continue to work on that at home....roleplay or use reminders, or, the next time they interrupt more than once, give them a consequence: "If you interrupt me again, you will sit against that wall until I am done and whatever you are asking for, be assured you will NOT get it." But I am mean like that, and my kids know that interrupting will cause negative attention from me, and nobody in my family wants that
And since I have always gotten feedback from teachers, other parents, family, etc that my kids are very well-mannered and behaved, and enjoyable to be around, I guess it is working....
It is our job as parents to raise our children to grow into adults who are responsible, productive, contributing members of society through teaching them honor, integrity, kindness, and patience. It is not our job, IMO, to hover over them to catch every need and want so we can immediately satisfy it before they grow a little uncomfortable. Have you happened to come across any studies lately on depression and anxiety rates in the teen/early adulthood age range in America? Rates are through the roof, and many child psychologists attribute this to helicopter parenting and instant gratification.
Waiting for adults to finish a conversation is a wonderful way to expose our kids to the art of delaying what they want for a while and still living to tell the tale. They will be Ok, I promise.