Has anyone had success doing this? I usually play as a total goody-two shoes, but lately I'm becoming more and more interested in using Barbarians to make the early game easier, and maybe adding Magicians to the mix later on. I haven't tried it extensively but it looks like the morale penalties get really vicious really quickly, even if you avoid the extreme alignments.

It can be useful, need some workaround.
From my experience - using 1-2 healers in barbarian/thug/demon herd means 1-2 morale penalty to fighters and ~6-8 to healers. But you don't care about healer morale - they just heal and provide global map regeneration. And fighters can get big morale boost from chopping meat.

If you hire Fairy in demon army - everyone get morale penalty. But even then her haste makes your army more effective than morale boost without her.

I remember in campaign that my first unlocked T3 unit was an executioner. I had pure light karma and fairy. Executioner had -10 penalty. (1 base morale) I needed to pick 2 medals with morale boost so he could do things.

How did you pick medals for him if his morale was so low?

I took executioner for scout and attacked free settlement.
Killing enemy unit with range attack gives +1 morale to your units near target.
I sniped 2 or 3 militia, then executioner started to deal damage on his own. Killing in melee gives +2 morale.
He finished with something like 20-25 morale.

I regularly use barbarians early game, they're much better than anything up to swordsmen, that you can only get if you have a good income. Barbarians are also more useful in early ruins, swordsman are better defending than attacking. Barbarians + healer is a good early combo, sometimes I hire an assassin if I don't have guardsmen yet. Once I have iron and guardsmen, I go for guards+swordsmen+healer, just because of the karma penalty you take when you hire barbarians. At the beginning they are invaluable, anyway.