What do you call a generic person?

conformist - a person who adopts the attitudes, behaviour, dress, etc of the group to which he belongs.

(Source)

I think average people come close to your definition: (from TFD)

• Usual or ordinary in kind or character: a poll of average people;

Idiomatic expressions for:

average people: (AmE)

• The terms average Joe, ordinary Joe, Joe Sixpack (for males) and ordinary, average, or plain Jane (for females), are used primarily in North America to refer to a completely average person, typically an average American.

average people (BrE)

• Fred Bloggs or Joe Bloggs, Joe (or: Jane) Public, John Smith, the man in the street, the man on the Clapham omnibus, 'Tom, Dick and Harry'. In Wales: Dai Jones.

(from Wikipedia)