So I got on and I was naked, just in my white fur, so I decided to put my stuff back on and it said it was already on, so I took it off and when I got to put my moon tail item back on it completely made my outfit disappear again, yet it said all my items were still on me.

Oh that's just a glitch, try removing any one of your accresories, you see everything else BUT the one you took off, if you do an action you will see your outfit and it only appears on your screen, you don't seem naked on anybody elses.reloading the page might do the trick or if not, just wait for sometime, maybe for 24 hours, your outfit will be shown again :)
Edit : Also don't worry if its still coming, remembered having that glitch for 3 days ()__()