Those who are not or will not be loyal to the Constitution won’t take that oath.... therefore, they can’t vote.
That goes for those who are up-front about what they believe.
Someone truly subversive would hide his or her true convictions to be able to subvert the government from with in.
The other problem is that they wouldn't be swearing allegiance to the Constitution as you understand it, but to the Constitution as they understand it, and when people have their mind set on something they don't admit that the Constitution stands in their way.
Finally, the way the country is now, I don't see something like this going through -- or if it did, it would be repealed or overturned by the courts a few years later.
Now I see your problem. You're just naive. They'd take the oath and take it about seriously as Kim Kardashian took that "Til death do us part" part of her vows.