The case was decided 6-3, with Gorsuch (who wrote the majority) and Roberts joining the liberal justices. The primary question is whether the Civil Rights Act's prohibition on sex discrimination in hiring/firing applies to these cases, and the Court finds that it does.

The statute’s message for our cases is equally simple and momentous: An individual’s homosexuality or transgender status is not relevant to employment decisions. That’s because it is impossible to discriminate against a person for being homosexual or transgender without discriminating against that individual based on sex.

The majority gets there by noting that sex just needs to be one "but-for cause" or the firing. In legalspeak, a "but-for cause" is something without which something else wouldn't have happened. But you can have more than one of these, and the majority in this case says that since you can't separate discrimination based on sexual orientation without also having discrimination based on sex, sex discrimination is a "but-for cause" and therefore in violation of the law. The reasoning goes like this: if you have two employees who are attracted to men, one male and one female, and you fire the male, you are treating him differently than a female employee because he's male. If he'd been female and attracted to men, presumably he wouldn't have been fired, and therein lies the discriminatory act.

The Court notes that the law only applies to individuals, not groups, so the fact that all homosexual men are treated similarly by a company wouldn't change the outcome.

Most of the majority opinion is spent explaining why, no really, we shouldn't be looking beyond the words of the actual statute. From this and some other opinions he's written, I get the feeling Gorsuch has some issues with the other conservatives' approach to statutory interpretation (not without reason).