They argued, I believe, that Sex originally meant with penis or with vagina.  So they argument is about original intent of the law... and if Congress wants to cover other meanings of sex (gender), they can pass a law doing as such. Of course, "intent" is a fuzzy word, even if Madison pops in and says otherwise.  
The original word might have meant "X", but the law intended to reduce gender based discrimination and our understanding of such a concept has expanded greatly. It would seem obtuse for SCOTUS to rule that the inclusion of this protection should be limited to others when the original intent was broader (not stricter protection).  After all Alito, if Congress meant to allow discimination of LGBT people, Congress could pass a law.
		
		
	 
In case anyone cares, the actual arguments are here:
https://www.supremecourt.gov/opinions/19pdf/17-1618_hfci.pdf
		 
		
	 
Like I said:
	
		
			
				Justice Alito dissent said:
			
		
	
	
		
		
			<a bunch of stuff not like what JH said>
		
		
	 
		 
		
	 
The original intent of the law was not in dispute -- both sides agreed that the 1964 Congress did not intend to ban discrimination against gay or trans people.  Whether original intent of the law should be the deciding criterion for the court was also not in dispute -- both sides agreed that original intent is irrelevant.  Whether it is appropriate for the court to expand the meaning of "sex" to align with modern understanding of it was also not in dispute -- both sides agreed the SCOTUS has no authority to do that.  Whether the government should protect LGBT people from discrimination was also not in dispute -- both sides agreed that it should.
This was a technical dispute over the reasoning principles courts ought to use to figure out whether the wording of Title VII logically implies that it's illegal to fire people for being gay or trans, going by the way those words were commonly understood in 1964.  Both sides agreed that if that wording has that implication, then the Court must protect gay and trans people from being fired for it.  Both sides agreed that if that wording does not have that implication, then the Court must not protect gay and trans people from being fired for it, and it's a modern Congress's job to pass new legislation to protect them.  Both sides agreed that both sides' shared desire for gay and trans people not to be fired for it isn't enough to give the SCOTUS the legal authority to stop it.  And both sides agreed that Congress's purpose of broadening worker protections does not authorize the court to make up whatever further broadenings it pleases.
	
	
		
		
			Poor Alito, the expansion of human rights must sicken him terribly.
		
		
	 
No, the expansion of human rights does not sicken him.  He wants human rights to be expanded.  Alito's concern in this case is with stopping the U.S. government from evolving into an operation more like the government of Iran -- a country without separation of powers, where democratically elected legislators are not an effective check on an imperial judiciary.  He perceives the court majority to be turning America into a theocracy where unelected judges are able to impose the tenets of Progressivism on the country without the people getting a vote about it.  And he perceives Gorsuch's argument that the 1964 law 
already forbade discriminating against gay and trans people to be mere window dressing, not the majority's real reason for their ruling.  He thinks their real reason is they want human rights to be expanded, and they're engaging in an unconstitutional power grab to expand them.  He's fighting them, 
even though philosophically he is sympathetic to their aim, because he doesn't believe the ends justify the means and he's against unconstitutional power grabs.
Alito is in the wrong, of course.  But the reason he's in the wrong is that Gorsuch's argument, window dressing or not, is legally correct.  Maybe the majority really are engaging in an unconstitutional power grab.  But if they are, Bostock v. Clayton County isn't the case they're doing it in.
	
		
			
				Justice Alito dissent said:
			
		
	
	
		
		
			Title VII of the Civil Rights Act of 1964 prohibits employment discrimination on any of five specified grounds: “race,color, religion, sex, [and] national origin.” 42 U. S. C.§2000e–2(a)(1). Neither “sexual orientation” nor “gender identity” appears on that list. For the past 45 years, bills have been introduced in Congress to add “sexual orientation” to the list,1 and in recent years, bills have included “gender identity” as well.2 But to date, none has passed both Houses.
Last year, the House of Representatives passed a bill that would amend Title VII by defining sex discrimination to include both “sexual orientation” and “gender identity,” H. R.5, 116th Cong., 1st Sess. (2019), but the bill has stalled in the Senate. An alternative bill, H. R. 5331, 116th Cong.,1st Sess. (2019), would add similar prohibitions but contains provisions to protect religious liberty.3 This bill remains before a House Subcommittee.
		
		
	 
Alito didn't point out this history as an argument that Congress didn't intend to ban discrimination against gay or trans people.  He pointed it out as an argument that the phrase "discriminate because of sex" is commonly understood to not cover discriminating because of sexual orientation or gender identity.
	
	
		
		
			Because no such amendment of Title VII has been enacted in accordance with the requirements in the Constitution (passage in both Houses and presentment to the President, Art. I, §7, cl. 2), Title VII’s prohibition of discrimination because of “sex” still means what it has always meant. But the Court is not deterred by these constitutional niceties. Usurping the constitutional authority of the other branches, the Court has essentially taken H. R.5’s provision on employment discrimination and issued it under the guise of statutory interpretation.4 A more brazen abuse of our authority to interpret statutes is hard to recall.
		
		
	 
Opponents are rarely the cartoon villains people like to paint them as.