Two people have to agree for a person to be nominated for a position on the Supreme Court: the President and the nominee. We can ask the same question about each of them: Under the current circumstances what kind of person would tender or accept the nomination?
We know the answer for President Trump: a person who puts personal, careerist, and narrow partisan interests ahead of a concern for the national interest -- in everything he does, including both moving forward on a nomination and choosing the nominee.
We don't know who the nominee will be, of course, but mightn't we entertain the question and answer in advance? A person who accepted the nomination under the current circumstances would by that act show that he or she puts personal, careerist, and narrow partisan interests ahead of the national interest. (I should note that we won't know, except by means of leaks, whether anyone to whom feelers are extended would decline to allow his or her name to go forward because the person thought that allowing it would be, as I put it earlier, dishonorable.)