"Naïve" vs "Ignorant"
Solution 1:
Naive has less of an association of being willfully misinformed. There are many usages e.g. "naive Bayesian", but the appropriate definition here is:
- marked by unaffected simplicity: artless, ingenuous... 2. deficient in worldly wisdom: credulous
Ignorance can reveal itself when a person unquestioningly sticks to a particular view point, due to an unwillingness or inability to consider alternatives. Ignorance
results from or shows lack of knowledge or education; lack of intelligence or awareness
The person described in the question could be both naive and ignorant. Naivete can be due to an unsophisticated world view, or unrealistic outlook from a lack of practical experience. But that doesn't have negative associations. I think ignorant would be the most well-understood way of describing a person with the attitudes mentioned.
Instead of naive, consider provincial, as that has negative connotations and is better matched with ignorant.
Solution 2:
Being "ignorant refers to a lack of knowledge. Being "naive" refers to a lack of understanding.
An ignorant person (factually) might nevertheless have great understanding and therefore not be naive. Think of the Scarecrow in the Wizard of Oz.
A well-informed (non-ignorant) person might also be naive because s/he doesn't understand things. Maybe the Cowardly Lion is in this category.
Solution 3:
Ignorant has a strong negative connotation and means that a person doesn't know things that they should know. Naive has a more neutral connotation and generally indicates a person who isn't familiar with the way the world works. Naive can sometimes even have a positive connotation and mean someone who hasn't been jaded by the negative realities of the world. Naive people are likely to be trusting or unsophisticated.
Essentially, ignorance is a lack of knowledge or education. Naivety is a lack of experience and wisdom.
Someone who makes inappropriate comments would more likely be described as ignorant. Someone who thinks that bad things only happen to bad people would be described as naive.