Minsc is a Ranger otherwise he would not have an Animal Companion in Boo.
What happened is he took a knock to the head (his big purple mark is a scar not a tattoo), and became essentially a 'fallen Ranger' and lost most of his brain cells, but gained berzerker rage.
Boo really isnt an animal companion... Anyone can buy a hamster. I have a lot of fondness for the character, but he was a ranger in name only, as they didnt have a barbarian class. The Folk Hero background provides Animal Handling and Survival skills and is perfect for him. Add in totem barbarian or something and he's essentially got everything he had in the original BG games. Minsc has a 6 wisdom in those games... I dont even think he could cast ranger spells in 5E.
