If you have an iPhone, you can flag certain contacts as allowing "Emergency Bypass". This lets their calls (and text messages if you flip another switch) vibrate and/or ring your phone even if you're in do-not-disturb mode.

Can't speak for Android, but I'm sure it has a similar feature (and due to system access it allows third-party apps, maybe you can do the same for third-party chat apps as well).

Worth noting in iOS any contact may bypass DND by calling twice in quick succession even if the contact isn’t starred.

In DND settings, there’s also option called “Allow Calls From” which user can choose from:

  >Everyone
  >No One
  >Favourites
  >Specific Group

In Android, you can have starred contacts. Only their calls will get through.

In Android you can configure Do Not Disturb to allow notifications from specific apps. I'm very curious if iPhone can do this.