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What happens if the spare the dying cantrip is cast on a Zealot barbarian using Rage Beyond Death?

Would being stabilized mean he doesn't need to make death saves until he is attacked again?

The spare the dying spell will set a character's number of death saves to zero, even a Barbarian that is Raging Beyond Death

The Rage Beyond Death feature (XGtE, p. 11) states:

While you're raging, having 0 hit points doesn’t knock you unconscious. You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends, and you die then only if you still have 0 hit points.

The spare the dying spell states:

You touch a living creature that has 0 Hit Points. The creature becomes stable. 

It only requires that a creature be living, not necessarily unconscious.

The section on "Death Saving Throws" states:

Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don’t need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any Hit Points or become stable.

Thus we know that stabalizing the Barbarian would change their number of death saves to zero.

There is a point of uncertainty though due to the following phrase:

[...] If you would die due to failing death saving throws, you don’t die until your rage ends, and you die then only if you still have 0 hit points.

It's unclear to me what would happen if a Barbarian got to three failed death saves and then spare the dying was cast on them. Clearly their number of failed (and succeeded) death saving throws would reset to 0 as they are still a valid target of the spell, but what would happen when their rage finally ends?

Would they fall unconscious because at one point they had three failed death saves?

Or would they fall unconscious only if they have three failed death saves when their rage actually ends?

I would say that RAW it is the first interpretation because the feature states "if you would die... you don't die until your rage ends" which is (nearly) equivalent to "if you would die... you die when your rage ends" and because there was a time where they would die, they automatically die (fall unconscious) when their rage ends.

As a GM I would say you need to have three failed saves when your rage actually ends.