Here is an article in the Jurist discussing the discrimination gay people face in the criminal justice system. The article primarily examines the harm that arises with jurors who have a gay bias. The article advocates for the SCT to take up the case of Charles Rhines v. Darin Young. The petitioner, Charles Rhines, claims that the South Dakota jury that sentenced him to death harbored an anti-gay bias.
As a general rule, courts don't like to interject themselves into the jury deliberation process. However, in 2016, the SCT in Pena-Rodriguez v. Colorado overturned a defendant's conviction because members of his jury harbored racial biases against Latinos. If the SCT were to take up this case and side with the petitioner, it would most likely be viewed as an extension of Pena-Rodriguez to sexual orientation.
Jurist.org: Anti-Gay Bias Has No Place in Our Juries