Earlier quoted context omitted.
I strongly disagree. Maybe it's an age thing, a "head of household" thing, or just an A(u)DHD thing - but I've definitely been in places in my life where I didn't have time to do anything discretionary. To put it another way - if they're willing to ask you to schedule time to talk to them, they're already violating social norms. Why would they bother to give you a way to get ahold of them if they didn't value the rel…
Making demands about how you want to be contacted when the group has been trying to include you for years is a dick move at minimum. You can say sorry I'll call you back in 10 if you are busy. Trying to dress this up as adhd/age/head of household (what is that even??) is just expecting the world to revolve around you No, learn to be a decent person.
I feel bad because in a few years that person might get laid off and realize they don't have any friends anymore.