Re-interpreting existing law is a HUGE component of our legal process. This goes all the way back to common law roots -- the court does not PREscribe law from above arbitrarily, rather it DEscribes the existing societal contract.
[0] Never mind that it also expects the existing case to be /exactly/ the same situation.
[1] Often just what anyone appealing to originalism wants them to have intended.
It is, but that doesn't necessarily mean it should be.
Decisions like this are ultimately political. The Court has basically decided that discrimination based on sexual orientation or transgender now counts as discrimination based on sex and hence is prohibited by law. But decisions about what real-world actions count as what legally recognized actions are political decisions, and political decisions in a democracy are supposed to be made through the democratic process, i.e., by the people or their elected representatives.
> This goes all the way back to common law roots
Yes, but those common law roots are not based on democratic norms; they come from societies that were not democracies but monarchies. A case could be made that our concept of "common law" has not kept up with the evolution of our society from monarchy to representative democracy.
Of course, an opposing case could also be made that even though our society is nominally a democracy, that doesn't necessarily mean that everything in the law should be democratically decided. Our law does recognize fundamental rights that cannot be changed or removed by the democratic process, and at least part of the process of common law is supposed to be to provide a way for people to have those rights recognized and respected even if there is no explicit statute that does so. Then the question would be whether there is such a right not to be discriminated against based on sexual orientation or transgender.
No, the majority opinion is not doing that. It is not arguing that "sex" includes "sexual orientation". It is arguing that, in order to discriminate based on sexual orientation (or transgender), you have to also discriminate based on sex.
The dissents disagree with that argument. But both sides agree that "sex" does not include "sexual orientation"; they are distinct concepts.
With that said, I still think that this is far from the Judiciary system amending legislation.