I think it is best not to be impolite.
Is the above sentence fine, or should it have
better instead of
best in it?
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Your sentence is correct. In Oxford English Dictionary one of the meanings of BEST is "most appropriate, advantageous, or well advised". Compare your sentence with the following: it's best if we both go.
That sentence is correct. I don't see much difference between that and
I think it is not to be impolite.
It is not either/or because both essentially have the same meaning, though the use of best is a little stronger than better.