What would be a word for describing a tendency to take the literal meaning of words above the accepted meaning?

For example someone accused of homophobia would answer that isn't correct as he is not afraid of homosexuals. The accepted meaning of homophobia is, of course, a much wider range of negative attitudes, least of them being actual fear.

What would be the term for such a person?

We do have a term for that: literal-minded, "tending to take words and statements in their literal sense". In earlier times, however, that phrase meant "unimaginative", though I have not seen it used that way for decades.

• His editing precision was legendary and he was so literal-minded that he even corrected literary quotations.
• They were certainly Gulliver's heroes, but were they Swift's? George Orwell wrote that when he read Gulliver's Travels as a child, he was so literal-minded as to think so.

Edited to add, the noun form is literal-mindedness (with thanks to PLL).

Stanching An Epidemic Of Literal-mindedness

The above is the title of a news article examining why our government — many of whom are lawyers, who use language differently than the average citizen — does not communicate well with the populace. Remember Bill Clinton and his infamous answer: it depends upon what the meaning of is is.

Pedantic

People who are pedantic are frequently excessively literal minded.