You can appear offline through your xbox live profile. Mirrors to any game you play as well.
Not sure if it's possible and how it works on PS4 though.
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Yeah, on PS4 you can set the PSN to appear offline but the game it's self will always show friends & clan that you are on destiny under roster no matter your PSN settings. All other games I have played do not do this but D2 does. It also shows you playing D2 on the app as well.
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That's weird. Works fine on xbox.
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I may have to get an XBOX then. Wish it worked that way on PS4.
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Tbh you still show up on the roster when you appear offline. It will show your name as black instead of grey and people can still join fire team if you have fire team settings open join. It's kinda mean.