No, the government can't. Try again
You can have restrictions to rights. Can't scream fire in a crowded theater. But rights are rights.
What do you mean "they can't". The govt CAN do things that are unconstitutional. They've done plenty of them. You know, like how the Supreme Court overturns things that the govt did previously, they even overturned their own decisions.
So, they can, doesn't mean it's constitutional. That's different. However take things like Dred Scott, it was there, it existed, in theory it was unconstitutional but was the law of the land for ages.
Rights are rights and right can be infringed, the govt can even tell itself its infringement isn't an infringement.
They can even say there isn't a right to marriage, or one part can say there is and another can say there isn't.
Go figure.