Peter Pedant
I would disagree...one can be ignorant, without being stupid.
However, if someone bases their opinions on their ignorance, then they will indeed be 'stupid'.
Good example - last year, someone on AB tried to claim that young British black, Asian and white kids all spoke with a West Indian 'patois' accent.
This was what the poster believed, but because they were ignorant of what West Indian accents actually sound like, in comparison to say, the accent of Adele, Tinie Tempah or Dizzie Rascal, all of whom share similar brogue constructs, they were simultaneously ignorant and stupid.
However, if they simply believed this, without trying to put it forward as a fact, they would simply be ignorant - not stupid.