Tennessee Williams' works can be defined as both Realistic and Naturalistic. Realists wished to show life as it was (defined through common characters, common settings, and an objective stand by the author). Naturalists were very much like realists, but they tended to include the power of nature as a "character" as well (personifying nature to show the challenge to mankind).
Given that visceral themes tend to be associated with emotions and feelings, rather than the intellect, Willliams' works were visceral. The character in his texts were those who stood on the brink of disaster. For example, in his play "A Streetcar Named Desire," Blanche, Stella, Stanley and Mitch were all character who had very deep-rooted issues. Blanche could not face the fact that she was aging. Stella was accepting of the emotional and physical abuse she suffered at the hand of her husband. Stanley was too much of the man's man (thinking that he could do whatever he wanted without consequence). Mitch was a "mamma's boy," too enveloped in his mother to truly look out for himself.
Therefore, the nature of the visceral themes in his works were designed to mirror the emotions and problems seen in real life, as they really were, without the author trying to change life for the characters. Williams accepted that life was not all roses, and his works depicted this. The violence, alienation, and false realities of life were the core themes Williams focused upon. These themes are simply too emotionally charged to be anything but visceral.