Words or phrases that describe a person who knows the answer to a problem but is not believed

I would argue that Cassandra does work here: the name is often used metaphorically, in a variety of fields. For example,

achieving a clear, shared vision in an organization is often difficult due to a lack of commitment to the new vision by some individuals in the organization, because it does not match reality as they see it. Those who support the new vision are termed ‘Cassandras’ – able to see what is going to happen, but not believed.

(same Wikipedia source linked above)

While Cassandra does have connotations of having to do with the future, any solution to a present problem is, by definition, a future thing. Someone who posits a solution is predicting that their solution will solve the problem. And failure to agree with a solution (that, we stipulate, would turn out to solve the problem) is most likely due to a failure of perception: either the perception that the person offering the solution isn’t worth listening to, or that the problem and/or its solution would work out differently than they will.

Not strictly a description of the person, but...

Falling on deaf ears

if a request or advice falls on deaf ears, people ignore it.

Warnings that sunbathing can lead to skin cancer have largely fallen on deaf ears in Britain.

Link