I have tried everything I have found online and all the settings are in place. My wife can invite me to calendar events, reminders, shared albums etc. I, however, with the same settings I can not do it from any of my two iPhones or my Macbook.
I would guess it is a problem with my iOS account itself, but I do not know where the problem is.
Could it be it that I do not have an @iCloud account? My Apple ID is my gmail account.