Someone in my party has a paladin\Barbarian, can they smite while Raging. You can't cast a spell while raging, but can you convert one into a smite?

Smiting isn't casting a spell.  Rage and Smite don't conflict at all.

RAW Yes, you can. Although it uses a spell slot, smites are not spells. They are class features fueled by spell slots.

A Barbarian cannot cast spells (take the [Tooltip Not Found] action) while raging, nor can they Concentrate on a spell while raging. As long as it wouldn’t violate ether of those prohibitions, a Barbarian could do anything else they want with their spell slots allowed by any feature, trait, feat, or other source. For example, if they had 2 levels in Sorcerer they could convert spell slots to sorcery points and vice versa while raging. Or if they had 3 levels in Ranger they could spend Spell Slots for Primal Primeval Awareness if they wanted to. (I don’t know why they would, but they could.)

Perhaps by RAW a Barb/3Ranger could do that, but they need to focus (a synonym of concentrate) for both an action and a bonus action when your character can't concentrate just for an action because he's so angry? I'd be unhappy about it (as DM) and would either say that they can't or permit it that one time and then houserule against it.

Quote from Linklite >>

Perhaps by RAW a Barb/3Ranger could do that, but they need to focus (a synonym of concentrate) for both an action and a bonus action when your character can't concentrate just for an action because he's so angry? I'd be unhappy about it (as DM) and would either say that they can't or permit it that one time and then houserule against it.

 
Rage specifically states:

 

Rage

In battle, you fight with primal ferocity. On your turn, you can enter a rage as a bonus action.

While raging, you gain the following benefits if you aren’t wearing heavy armor:

• You have advantage on Strength checks and Strength saving throws.
• When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.
• You have resistance to bludgeoning, piercing, and slashing damage.

If you are able to cast spells, you can’t cast them or concentrate on them while raging.

Your rage lasts for 1 minute. It ends early if you are knocked unconsciousor if your turn ends and you haven’t attacked a hostile creature since your last turn or taken damage since then. You can also end your rage on your turn as a bonus action.

Once you have raged the number of times shown for your barbarian level in the Rages column of the Barbarian table, you must finish a long rest before you can rage again.

You know all those features that state the character “must Concentrate (as if on a spell)?” Primal Primeval Awareness is distinctly lacking that phrase. The PHB has had 5 separate errata publications since it’s initial publication. if they wanted that feature to preclude interacting with Rage, they would have changed “focus” to that magic phrase. Not many people use Primal Primeval Awareness anyway, because the spell slot is typically worth more. Why alienate people further by eliminating the one positive interaction it has?

I've already discussed pretty much everything you've said.

As for your closing question, that's an argument against rules in general, not just my decision. Why deny the one positive interaction between casting spells and rage? Like all rules, it is because of one or both of three reasons - it's OP otherwise, it's unthematic or it is inconsistent.

Either way, you are houseruling that a Barbarian cannot be “Primally “Primevally Aware” while Raging. If anything, the name alone makes it thematic enough for me, and the fact that they can do it RAW means it’s a houserule to treat it otherwise. You do you, I’ll never begrudge anyone their houserules. Your table, your rules. But it’s not RAW, nor do I ever believe RAI. 

IamSposta, I was reading this thread and it didn't make sense. Then I realized you meant Primeval Awareness, not Primal Awareness. I could see how Primeval Awareness would be fine with Rage, but Primal Awareness is not. It requires casting a spell, just doesn't use a spell slot.

Quote from ThriKreenWarrior >>

IamSposta, I was reading this thread and it didn't make sense. Then I realized you meant Primeval Awareness, not Primal Awareness. I could see how Primeval Awareness would be fine with Rage, but Primal Awareness is not. It requires casting a spell, just doesn't use a spell slot.

 
Ah yes, quite right. Thank you.

Just another example of Crawford not learning his gorram lessons time and again. One would think he might have learned by now to not keep naming stuff like that. I mean, it’s not as if people haven’t been complaining about the whole plethora of “weapon attack,” “attack with a weapon” malarkey for half a decade or anything. 🙄

Yeah...

Natural Explorer > Deft Explorer

Favored Enemy > Favored Foe

Primeval Awareness > Primal Awareness. 

Can't blame anyone for getting confused on which is which on the ranger optional features. 

As for rage/smites I'd allow it in my games if I had a barbarian/paladin multiclass. Not any of the smite spells of course, but divine smite itself sure. 

After reading this thread I wish that a Barb/Paladin wasn't utterly MAD because the idea of 'I'm so angry that my hits carry DIVINE POWAH!' sounds really cool!

Along that vein, I've tinkered with a Cleric/Barb because many of the Cleric traits aren't spells either.

Smite is not a spell, and Paladin spell slots are fueled by their force of will as opposed to divine, natural, or arcane forces. I have no problem with a Barbadin smiting while raging. In fact, I rather like the flavor.

Quote from Darkaiser >>

After reading this thread I wish that a Barb/Paladin wasn't utterly MAD because the idea of 'I'm so angry that my hits carry DIVINE POWAH!' sounds really cool!

Along that vein, I've tinkered with a Cleric/Barb because many of the Cleric traits aren't spells either.

 It doesn't have smites specifically, but you could look up path of the zealot barbarian if you want a sort of crusading 'holy barbarian' type character. Including once a round getting to deal extra radiant damage on a hit. (Or necrotic if they pick it over radiant.)