You cannot benefit from the racial feat if your race changes
Page 165 of the PHB says:
You must meet any prerequisite specified in a feat to take that feat. If you ever lose a feat's prerequisite, you can't use that feat until you regain the prerequisite.
The racial feats in XGtE all have a prerequisite that specifies the race that can take them. For example, Bountiful Luck has the Halfling prerequisite.
Therefore, if you are no longer a halfling because of reincarnation, then you cannot use the benefits of the feat.
But you will regain the use of the feat if your prerequisite race is restored
As the quote from the PHB says, you can regain the feat's benefits if you regain the prerequisite. So, if something turns you back into whatever race the racial feat requires, you regain the benefit of the feat.
In your example, if you are a halfling, die, and are reincarnated as a dwarf, you would be unable to benefit from the Bountiful Luck feat. But if you then died again and were reincarnated back into a halfling, you would regain the use of Bountiful Luck because you are a halfling again.