I think you are misreading what he is saying. The first amendment has two separate clauses related to Freedom of Religion: the Establishment clause and the Free Exercise clause. Scalia is saying that if the State establishes a religion, but this establishment does not interfere with the Free Exercise of anyone’s religion, he doesn’t think that individuals should have standing to bring suit, because they have not been harmed. Here I think Scalia is attacking judge-made Establishment doctrine, as opposed to the Constitution’s Establishment clause. Now it’s true that Scalia’s interpretation would make it difficult to enforce the Establishment clause, but there are questions of standing (as well as the problem of inadequate remedies) that make it somewhat difficult to enforce other parts of the Constitution as well.
In neither of the VRA or ACA cases did Scalia write an opinion. In the VRA case (Shelby County v. Holder), which was decided 5-4, he joined four other Associate Justices in Chief Justice Roberts’s opinion. In the ACA case (National Federation v. Sebelius) there was a split 4-4-1 decision with Roberts casting the deciding vote and Scalia joining an unsigned opinion. Scalia was hardly out in left field on either case, as he was part of the majority in Shelby and joined three other Justices in Sebelius, and neither of these cases really say anything in particular about his jurisprudential approach since he didn’t write an opinion for either. If you want to attack Scalia based on the way he voted in these cases, you’ll also have to attack those who voted with him… and I don’t think anyone is accusing Kennedy of being some undemocratic religious nutcase.
But let’s look at the cases anyway.
The opinion on the VRA was predicated on the fact that the preclearance formula being used today was last modified almost 40 years ago in 1975. (Preclearance means that affected states must clear their voting regulations with the federal government before the voting regulations can be implemented.) The majority Roberts opinion said that the formula for determining what states are covered by the preclearance requirement must change to reflect changes in the level of discrimination, especially since the constitutional justification for the VRA was to remedy prior discrimination: if the Court was to judge the 1975 preclearance formula in the current context, it would be found unconstitutional. The idea of preclearance was not struck down, only the 40-year-old formula for determining what places are affected. The opinion makes it clear that not only is Congress free to draft a new preclearance formula, they are encouraged to do so. (Of course, it is extremely unlikely that the requisite bipartisan support for a new preclearance formula can be found, but what the Court is doing is essentially re-punting it to Congress to make a decision).
The unsigned joint dissent in the ACA case looks at the language of the ACA, which specifically says the ACA is not a tax, and concludes that the mandate should not be interpreted as a tax. If it is not a tax, then 5 Justices agree that it fails the Commerce Clause and would be unconstitutional. But the ACA was saved only because Roberts (writing in a separate opinion that no one else joined) said that even though Congress explicitly said it wasn’t a tax, it really was a tax, and was thus a constitutional exercise of the federal government’s taxing (and spending) powers under the 16th Amendment. So that means 5 judges would have rejected the law as an unconstitutional exercise of the Commerce Clause (because you cant use the Commerce Clause to force people to engage in commerce), while 4 justices (including Scalia) also say that because it isn’t a tax and doesn’t claim to be a tax, it cannot be saved under the 16th Amendment.
NB: under the federalist system enshrined in the Constitution’s 10th Amendment, the federal government can only make laws in the specific subject areas enumerated in the Constitution, with all other powers being reserved for the states. For example, only the states can have general police powers. For everything the federal government wants to do, there must be a constitutional hook. In the VRA law, the 14th amendment was the hook. In the ACA case, both the Commerce Clause (which has become incredibly broad in since the New Deal) and the 16th Amendment were possible hooks. Absent one of these Constitutional hooks, the federal government cannot enact laws.
Note that the two cases that Olson was talking about were dealing with race-based discrimination. The 14th Amendment was written to apply to race-based discrimination. Everyone knew, at the time it was written, that it was about racial discrimination and emancipation. On the other hand, nobody reading the 14th Amendment in 1868 thought it was extending rights to homosexuals. This is how Scalia would differentiate the two. Scalia thinks that if we now want to extend similar protections to gays, we should either legislate that protection or amend the Constitution to reflect this.
If you want to argue further, please cite to opinions that Scalia actually wrote.