There’s a fine line, but it’s almost always possible to tell when you have crossed it.

1:
“I believe that god created man from whole cloth in one fell swoop, and the theory of evolution is crap” Stubborness.

“I believe that god created man from whole cloth in one fell swoop, and the theory of evolution is crap, and I’m going to try to prevent evlution from being taught” Stupidity.

2:
” I believe that the universe- including man, sprang forth from nothing. The natural laws wrote themselves, and the universe has no creator” Stubbornness.
” I believe that the universe- including man, sprang forth from nothing. The natural laws wrote themselves, and the universe has no creator, and I will do my damndest to prevent any mention of a creator in any form, anywhere, ever.” Stupidity.

3
“I believe guns are evil, and I would never have one in my house” Stubbornness.
“I believe guns are evil, and I would never have one in my house, and I’ll do my damnedest to prevent anyone else from owning them” Stupidity

See a pattern? You can have whatever bizzarre beliefs you want, and sticking to them in the face of overwhelming evidence to the contrary is just stubbornness. Inflicting that ignorance on others is stupidity. Perhaps even evil, depending on circumstances.

Your mileage may vary.