- race → racist
- freedom → fascist (for example)
- knowledge → ?
- disposition → ?
What's the word to describe a person who is disrespectful of your knowledge or disposition?
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Racist means "discriminatory against on the basis of your race", not merely "disrespectful towards". And fascist means a proponent of a specific political theory, not someone who is disrespectful of freedom. The answers provided above are valiant efforts, but there is really no answer to your question exactly as it's posed since it's based on incorrect assumptions.
My top suggestion for knowledge is probably philistine, someone who's uninterested in intellectual pursuits, or is smugly ignorant or indifferent to intellectual value. It's a bit of a stretch, but seems appropriate for the context.
You might also simply use ignorant, or there's a variety of terms for negative terms for "uneducated person" that could (again, at a bit of a stretch) be adapted to fit: rube, yokel, etc.
Also, people will debate the validity of a question in the comments; it's well within their rights here and the acceptable use of comments. Being hostile to people who question your question isn't appropriate.
A racist believes that one race is inherently superior to others. One who believes that one level or branch of knowledge is inherently superior to another is an elitist or, more informally, a snob (or perhaps an intellectual snob). I am not sure if these terms could be used for disposition, however.
Bigot could also be used, but it doesn't have the meaning of "X better than Y and Z because of inherent reasons" - it is "X is better than Y and Z because X is what I believe in".