When considering the requirements for a Long Rest, would maintaing Rage preclude someone from gaining the benefits of their Long Rest (if they were an Elf doing Trance so as not to go unconscious).
It doesn't matter
A rage cannot be maintained for more than one minute under any circumstances, according to this discussion. Because you cannot rage for the entire duration of the long rest, it does not affect your long rest.
Raging at some point during the long rest is ok, given that any combat shorter than one hour does not interrupt the rest either, and it's likely that a barbarian will rage during that combat.
Yes, it is a strenuous activity.
Note that Crawford's tweet does not state nothing stops you from Concentrating during a Long Rest - only a Trance. Trance can be done without a Long Rest, although there are few reasons to do so.
Additionally note that the long rest reference does not cover the inverse statement: "Can you gain the benefits of a Long Rest, while Concentrating."
A Long Rest is ended by doing something considered light activity for more than 2 hours, or strenuous activity for more than 1 hour.
Definitions of Strenuous activity:
A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours. If the rest is interrupted by a period of strenuous activity—at least 1 hour of walking, fighting, casting Spells, or similar adventuring activity — the characters must begin the rest again to gain any benefit from it.
Raging appears to be strenuous, and is certainly not less than light
Raging seems pretty close to fighting or similar adventuring activity, and at the very least seems at least as intensive as keeping watch, reading or talking. If standing watch, reading or talking for no more than 2 hours is enough to lose the benefits of a long rest, I find it hard to imagine it is possible to either Concentrate or Rage throughout the whole rest.
Additionally, casting a spell for more than 1 hour is considered strenuous activity. Note that casting a spell for longer than 1 action uses Concentration. Rage and Concentration cannot coincide at the same time:
If you are able to cast spells, you can't cast them or concentrate on them while raging.
This implies Casting Spells and Raging uses a similar level of focus or mental/physical energy, as they are mutually exclusive.
Conclusion: Raging (and by extension, Concentration) cannot be done during a Long Rest for longer than 1 hour, or in a more generous ruling, 2 hours, without breaking a Long Rest.