How can you be an anti-Semite without meeting a Jew? It’s like not liking butternut squash kugel or something because you’ve never tried it. Or being bad at tennis because you’ve never played it.
Then again, he may well have met Jews, comsidering that many of his plays are conjectured to have been written about his possible travels during his blank decade when he vanished. He apparently knew a lot of street plans and clothing styles of many cities because he visited them then. Perhaps he may have met Jews then.
Then there’s always the possibility that Shakespeare wasn’t written by Shakespeare, which would make it even more possible he was anti-Semitic.
Mishpacha had a really interesting article on the subject a year or two back.
It would be more plausible to say that Dickens was an anti-Semite than Shakespeare, and at least he eliminated the tens of references to Fagin being “the Jew” at some later point. He actually definitely met Jews.