All Oxfordians (people who believe "Shakespeare" was a beard/pen name for Edward de Vere) agree that Shakespeare was an actor, ie, "player." It's also well-known that acting was a low-status occupation in Elizabethan society, explaining why people mocked Shakespeare's coat of arms.
Writing, especially writing erudite verse in the Tudor court style, was not a low-status occupation in Elizabethan society. Anonymity/pseudonymity was not universal, but common.
So an Oxfordian would ask: why is Shakespeare, as a social climber, awarded arms for a low-status profession that's considered basically artisanal in caste, leading to general mockery, when in fact he practices the high-status profession of courtly playwright/poet?
Social climbers were not at all unheard of in the Elizabethan world. What is unheard of is a social climber who is not a social lion, whose resume is well-attested, whose presence and personality is constantly documented -- like, say, Ben Jonson.
Doctors say: when you hear hoofbeats, think horses. Maybe Shakespeare wasn't a social climber at all, but remained a country bumpkin his whole life, as he moved from stagehand to actor to what we'd now call a producer? Maybe the plays and sonnets read like late Tudor court poetry because they are late Tudor court poetry? Maybe, like much Tudor court poetry, it was written pseudonymously, not for publication?
The one coincidence that Oxfordians have to explain is how Vere wound up publishing under the name of this real individual, Shakespeare. Who (like Vere himself, of course) was involved in the theater world. Pseudonyms are typical in Tudor court poetry, but "beards" aren't.
My guess, an idea I've never seen anyone else broach for obvious reasons, is that Will Shakespeare's first occupation when he came to London was... male prostitute. Again, when you hear hoofbeats, think horses. Maybe Vere just thought this week's boy had a pretty name.
Here's some Tudor court poetry, by the way:
http://shakespeareoxfordfellowship.org/what-is-desire-by-edw...
Note the second stanza, which sounds exactly like Shakespeare to my ear. No one else from the period sounds like this. An Oxfordian would call this Shakespearean juvenilia.