Is the idea of a self-contradictory constitution - that is, a constitution which under one provision permits some state of affairs, but under another prohibits it - odd at all? The answer is, actually, no. Consider these examples:
Congress imposes a tax on the purchase of television ad time, but only for political ads. That's presumably perfectly okay under the tax power, but certainly a breach of free speech under the First Amendment.
A local police officer stops a black motorist who makes a turn without using her turn signal. The stop has an objectively valid basis and so under current interpretation would not violate the Fourth Amendment, which regulates "seizures," including stops. But if the reason for the stop was actually a deliberate program of racial profiling, it would be unconstitutional race discrimination under the Fourteenth Amendment's Equal Protection clause.
What about a state statute that provided for the death penalty for homicides, if they are committed by African-Americans? Clearly, even if the Constitution affirmatively declared that the death penalty is not unconstitutional under the due process clause (which permits the deprivation of life "with due process of law"), this statute would be unconstitutional under the Equal Protection clause. And that's true even though the Due Process and Equal Protection clauses are both in the same Amendment, the Fourteenth. (The Fourteenth Amendment's due process clause applies to the states; the Fifth Amendment'a due process clause applies to the federal government.)
But, one might say, even though the Constitution contains multiple provisions and those provisions naturally can have differing consequences for the constitutionality of particular government actions, at least those provisions' intersection must be determined in light of their original meaning. A provision can't somehow expand in meaning to swallow some situation it formerly didn't apply to.
This contention is of course just an instance of the general idea that the constitution's meaning was fixed at the time of its adoption. That's not my view, as I've made clear elsewhere, but I want to offer one more example of our law taking a different approach.
This is Bolling v. Sharpe, the case that held school segregation in the District of Columbia unconstitutional. Why didn't Brown v. Board of Education, issued the same day, decide this? Because Brown was a decision under the Fourteenth Amendment's Equal Protection clause, which applies only to states. There is no textual Equal Protection clause applying to the federal government. So how does Brown's command come to apply to the schools in D.C., which are not governed by the Fourteenth Amendment because the District of Columbia is not a state? The answer is: through the equal protection component of the Fifth Amendment's due process clause.
But how do we know that that implicit equal protection component applies to school segregation? After all, the Fifth Amendment – which itself has never been amended -- was adopted at a time when the Constitution explicitly, if euphemistically, “contemplated” (to use Scalia's language) slavery. The Thirteenth Amendment made slavery unconstitutional, so we can say that the Fifth Amendment no longer contemplates that, but what about school segregation? The Fourteenth Amendment – which the Brown Court interpreted as banning school segregation (though that may well not have been what the Fourteenth Amendment’s adopters thought it meant) – doesn’t apply to the federal government. What the unchanged language of the Fifth Amendment should be understood to “contemplate” now is the result of the Supreme Court's interpretation of the Fourteenth Amendment and the Court's conviction that “[i]n view of our decision that the Constitution prohibits the states from maintaining racially segregated public schools, it would be unthinkable that the same Constitution would impose a lesser duty on the Federal Government.” In short, the Fifth Amendment’s meaning grew over time to outlaw school segregation.
Justice Scalia's opinion in Glossip v. Gross takes for granted that because the constitution explicitly contemplates the existence of capital punishment, that penalty could not legitimately be held unconstitutional. But it turns out that’s simply not so.