The word "refuse" is an antonym of the word "accept"; does this make the phrase "refuse to accept" redundant and/or linguistically incorrect?
In some senses, yes. For example, "refused to accept the invitation" could be replaced by "refused the invitation" without a change in meaning (though I feel the latter is a bit more emphatic).
However, "accept" has many meanings, such as "to regard as true or sound." In this case, "refuse to accept the claim" does not mean the same thing as "refuse the claim." For example, if someone claimed that the Earth was flat, you could refuse to accept the claim, but not refuse the claim. "Refuse the claim" is typically used when claim means "a demand for something due" rather than "an assertion that something is true," e.g. "He refused the insurance claim."
No it isn't always redundant and yes it can be linguistically incorrect.
There are many nouns such that "to refuse to accept X" cannot be replaced by "to refuse X"
I refuse to accept your opinion/view/belief/thinking/stance/perspective/position/standpoint.
I refuse to accept your mediocrity/laziness/ ineptitude/lack of morals.
In none of the above can you drop the words 'to accept'.
To Refuse is both a transitive and intransitive verb.
I refuse | intransitive
I refuse your money | transitive
I refuse to accept your money | both, or ditransitive/bitransitive
Ditransitive verbs have both a direct and indirect object. In this case, the indirect object is
to accept and the direct object is
As far as I can interpret,
refuse to accept is in no way incorrect.
To answer the question, No. Having refuse and accept together does not make them "redundant" as you say. Nor does it make them contradictory. It's just a coincidence that they happen to be antonyms.
I love to hate you
I ask to answer you
I move to stop you
I agree to disagree with you