Clayton "Clay" Louis Hollingsworth is the brother of Blanche, Virginia, Charmaine and Tad Hollingsworth. He was portrayed by Monte Markham in two episodes of The Golden Girls, "Scared Straight" in Season 4 and "Sister of the Bride" in Season 6.
Clayton lived most of his life as a closeted homosexual and hid his orientation from Blanche and the rest of his family. Also, he seems to be the youngest of the Hollingsworth children, as Blanche affectionately calls him "baby brother". He was married to an unnamed woman for several years, but this marriage was his attempt to deny his homosexuality, until he couldn't hide it anymore.
When Clayton tells Rose that he is gay, she tries to help him to tell Blanche. Afraid to admit that he is a homosexual, Clayton claims that he slept with Rose. Clayton eventually tells Blanche the truth, and she has difficulty accepting it until she realizes during a heart to heart that he is still the same baby brother she has so much in common with. Sophia deduced he was gay with three questions: "What do you think of the Miami weather?" (Oh, it's lovely!) "Ever been in Europe?" (No, but it's always been a dream of mine!) "How many fingers am I holding up?" (Two?)
Clayton visited Miami to tell Blanche that he was getting married to very special "friend" Doug. She had a difficult time with the news, but she eventually accepted it.
This theory is from TV Tropes and should be taken as such
Blanche's reaction to Clayton's coming could be because of her roots as a Southern woman with religious background and the time the episode aired. At the same time in Series 1 and 2 she shows that she isn't Homophobic at all but maybe it's who Clayton is that effects her reason. Until the Golden Palace we were to believe that Blanche had Clayton as her only brother but then we are introduced to Tad, because of his disability Blanche had been told to treat Tad as a secret shame, so she saw Clayton as the most perilous so his Coming Out would be hurtful to her and thus she took it harder than other people.