But did he?

The thing is, theaters and actors were given a hard time by default.

Plays, in general, were criticized for a number of things, going from moralistic concerns to reasons which really look like little more than excuses. A popular scandal was that of young boys playing the role of women (as women themselves were banned from the stage), something that was said to encourage homosexual desire among the male audience. But plays were also criticized for making people lazier; keep in mind that there was no electric lighting, so plays always took place in the early afternoon, when there was still enough natural light to keep going for the whole three hours or something of their duration: hence your local carpenter calling it a day shortly after his lunch break to go see, or hear, the show. Theaters were seen as sinful places, because the Elizabethan audience was really varied, encompassing all social classes, even criminals and prostitutes; and the latter, of course, were accused of mingling with the crowd in order to attract new customers. Etc. etc.

Let's just say that theater was disliked because it had this unpleasant tendency to speak freely, while addressing a diverse audience (read: commoners), while "promoting" behaviors that could have easily been classified as devious in the religious eye (puritans in particular were die-hard haters). Unsurprisingly, plays were subject to being censored; theaters would often be temporarily closed because of "plague outbursts" (which were a thing, but also served as a handy excuse); and actors were always at risk of being arrested, usually under the pretense of them being vagabonds (they did wander around, but only because it was their job that required them to), unless they officially served under an aristocratic household (which is why companies tried and convinced lords to lend them their names, even though this was usually nothing more than a formality).

It is also no coincidence that the majority of theaters had been built (from the construction of The Theatre in 1576 onward) in the so-called liberties, that is, "special" neighborhoods which were technically situated in the city of London, but were also excluded from its jurisdiction, meaning that the authorities had no direct control on them. This is where all outcasts (outlaws, prostitutes, actors themselves, and in general all people with nowhere else to go) found their place, away from the "cleaner" parts of the city. You can read more about liberties and all of this theater ordeal in this Britannica article.

So basically, Shakespeare and other playwrights of his time had chosen the thug life the day they had decided to become actors really. Causing public disdain was on their job description.