What does Shylock say he will not do with a Christian?

Shylock makes it abundantly clear that he hates Christians and wants as little to do with them as possible. He'll do business with them—a man has to make a living, after all—but anything beyond that is strictly off limits. He certainly won't eat with Christians, not just because he wouldn't enjoy their company but because they'd insist on eating food that isn't kosher. As a Jew, Shylock would be forbidden from eating certain kinds of food such as pork, and yet it is just such food that the Christians like most of all. Any food eaten with Christians would not be prepared according to the strict dietary laws of Judaism, so eating with them is out of the question.
As indeed is drinking. Shylock has no desire whatsoever to socialize with Christians. They do not respect him; they treat him abominably because he is a Jew, so why on earth would he want to hang out with them? Ask yourself this question: would you want to spend time with people you knew for a fact hated you for your religion? Most people would say no, and Shylock is definitely one of them.