There are a few class features in the game that require concentration, but are not spells: A Trickery Cleric's Invoke Duplicity, a Glamour Bard's Mantle of Command, a Graviturgist Wizard's Adjust Density, etc. They are all phrased in a similar way concerning concentration:
for 1 minute, or until you lose your concentration (as if you were concentrating on a spell).
Going into a rage stops you from keeping concentration on a spell:
If you are able to cast spells, you can't cast them or concentrate on them while raging.
But, if a multiclassed character (with one of the above subclasses, plus barbarian) uses such a concentration-based feature then goes into a rage, are they able to maintain concentration on that feature?
For example: Timmy the Trickery Cleric/Barbarian uses Invoke Duplicity, then enters a rage. Is Timmy able to continue concentrating on Invoke Duplicity?
Best Answer
No, you can't, because they require concentrating "as if" on a spell
As you note, the barbarian's Rage feature says:
The Trickery Domain cleric's Invoke Duplicity Channel Divinity option says (PHB, p. 63; emphasis mine):
Because you need to maintain concentration on the illusion "as if you were concentrating on a spell", anything that prevents concentrating on a spell also prevents you from concentrating on something "as if" it were a spell.
Rules designer Jeremy Crawford unofficially confirms this interpretation in this January 2018 tweet, in response to a now-deleted question that specifically asks about the Invoke Duplicity feature:
Rage specifies that you can't concentrate on spells while raging; the same restrictions apply to things that require you to maintain concentration "as if you were concentrating on a spell". As far as I know, all official non-spell features that require concentration in this way specify that you do so "as if you were concentrating on a spell", and so Rage prevents the character from concentrating on any of these features.