ATC not recognising custom callsigns or tail numbers

No… it has nothing to do with the Xbox server issue.
This is how the priority for the items in the aircraft.cfg works namely in Tail number or Callsigns.

  1. The ATC Option from the World Map when you plan to start a flight takes precedence over everything. This means any text that you put will be used as the callsign or tail numbers and flight numbers too. If you leave any of this field blank, it will take the values coming from the next level down.
  2. The aircraft.cfg file that belong to your Livery. the atc_id is the tail number. And will always show with whatever value you put. This means that if your livery has a “hardpainted” tail number directly into the fuselage texture, the atc_id tail number will either double up or overlap. So you have to make this invisible by assigning atc_id=" ". Note that it’s NOT a space. Because if you put a space in there, it will freeze and stuck your sim. Instead it’s a valid character file that is generally blank/invisible character. The callsign and flight number will take from this aircraft.cfg when you leave the one at point 1 blank. If even this field is blank, it will take from the next level down.
  3. Aircraft.cfg file from Modded aircrafts in your community folder. So the atc_id, flight number, and atc_airline callsign will take from any modded aircraft in your community folder. This includes A32NX or any other modded aircrafts. If these are blank too. Then it will take the value from the next level down.
  4. Aircraft.cfg file from the default aircraft in the official folder. It will take the values from here.

So my suggestion here is review these values from the bottom up, make sure there’s no conflicting ones.

I myself, finds the liveries I downloaded, while they’re all awesome quality and very well done. Always have the wrong structure and aircraft.cfg files. So I end up with rehauling the entire livery. So that I only utilise their Texture folder. But everything else is standardised based on my preferred structure and the appropriate aircraft.cfg files. This means I use a proper callsign (without the all caps otherwise the ATC will start spelling them), flight number, and tail number.