They've provided MBTI typings for the Fallout TV series characters on Personalitydatabase site.
I'll provide my own interpretation:
-Lucy: an IxFJ, probably INFJ, as she has a naive idealism
-Maximus: an ENFP, naive like Lucy but with a tendency to distort the truth
-Siggi: an INTJ, morally upright stoic scientist, contrast his demeanor with other characters incorrectly typed as INTJ in the image attached.
-Moldaver: an ENFJ, at first I thought she was an ENTJ but she wants to provide for the people i.e. a socialist whereas the latter is a capitalist. In LoTR, she'd be Galadriel.
-Barb: an ESTJ, a lawful evil administrator, incorrectly typed as INTJ
-Norm: an INTP, I suspect he might turn evil/self-serving at some point
-Woody: an INFP, classic hipster guy, they keep mistyping them as ISFJs and vice-versa
-Robert House: I guess he's the true ENTJ, an entrepreneur capitalist/industrialist with long term vision
-Ghoul: Didn't put him in the image below but he's typed as an ESTP on the site but given his wife Barb is an ESTJ, I guess he must be a disheartened, sad ESFP in the wasteland. I suspect we'll see him save the day at some point when he finds something worth fighting for, like his daughter.