This will not affect anything in game.
What is happening is it is closing the Bungie profile that was linked to your PS account as it will not actually have a PSN ID linked to it anymore once you link your PSN ID to the Bungie profile your Xbox live account was linked to.
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Ok thank you for letting me know
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I would refer to Bungie's article here on merging accounts. You may wish to make sure you are keeping the Bungie profile you wish to keep https://www.bungie.net/en/Help/Article/12130