The "Anti-Straffordians" are those that contend that the man we know as William Shakespeare did not write the plays and poetry attributed to him.
Since William Shakespeare, from Strafford-upon-Avon, did not attend univerisity, these people question how he could have known and/or experienced certain things that show up in his plays. It is rather a snobbish attitude that believes that only a university educated person could have written the plays and other writings. This attitude does not take into account genius.
From the time he left Stratford until he showed up in London, little is known of his life and this period is called "the lost years". Speculation has him doing everything from sitting in on university classes and being a tutor to serving as a soldier and travelling over seas. We just don't know.
If, as they contend, Shakespeare did not write "the compete works", it is the biggest hoax and secret of all time and a lot of people where involved.
As far as I am concerned, William Shakespeare is William Shakespeare.