While I challenge your assumptions, as properly expressed by ZD and Wolf, you do pose a valid question. There may be cases in which the halachic Jewish ancestry is problematic. Knowing many shluchim and those who go on mivtza’im, I do not see any verification or investigation being done. I have no clue what the numbers might be, but it is something that should be explored.
Now, let’s assume there is a halachic non-Jew here. Is there an issur involved in putting him on tefillin? I doubt that. Anything wrong with providing this individual with Shabbos candles? Another doubt. Intermarriage – that is a great question. This question is relevant to the large population of Baalei Teshuvah and not specific in any way to Chabad.