Rappaport’s Law enforced strict segregation between the No-Maj and wizarding communities. Wizards were no longer allowed to befriend or marry No-Majs. Penalties for fraternising with No-Majs were harsh. Communication with No-Majs was limited to that necessary to perform daily activities.
Rappaport’s Law further entrenched the major cultural difference between the American wizarding community and that of Europe. In the Old World, there had always been a degree of covert cooperation and communication between No-Maj governments and their magical counterparts. In America, MACUSA acted totally independently of the No-Maj government. In Europe, witches and wizards married and were friends with No-Majs; in America, No-Majs were increasingly regarded as the enemy. In short, Rappaport’s Law drove the American wizarding community, already dealing with an unusually suspicious No-Maj population, still deeper underground.
Much like any
Muggle No Maj law, they are hoping the law itself will prevent most witches and wizards from breaking it. Considering the wizarding population really isn't that large (as a percentage of the total population), it is probably not that difficult for American Aurors to perform random inspections.
Would this prevent all marriages between No-Majs and Wizards? Probably not, but those that broke the law would have to live in seclusion and in fear that they would be discovered.
Then if discovered, the witch or wizard would be arrested and the No-Maj would be Oblivatiated as was required by International Confederation of Wizards of any No-Maj/Muggle exposed to the Wizarding World.
As President Rappaport was forced to tell the International Confederation of Wizards at a public inquiry, she could not be sure that every last person privy to Dorcus’s information had been Obliviated. The leak had been so serious that the after-effects would be felt for many years.