Isn't the whole thing with The Alters that they are just a ton of soul spirit thingies occupying one body and alternating who is in control, who's listening and talking, and who's not paying attention? Why not wear the shirt when eighter Sin or Reji is in control/backseating (if the shirt is clean ofc), and just not fight? If you really all do share one body, then you also share all physical belongings, so the shirt is for every one, Sin, Reji, Kindiling, Ms.Meowsy, You as in Uluri, and everyone else I fogot about!
...ot am I getting it wrong and missing the whole point?
Edit: WIATWAITWAIT I GOT IT! Buy a second copy of that shirt. That way these two can always know there is one specificly for them!