The due process is the felony conviction. The one that limits their "Life liberty and pursuit of happiness" by putting them in prison. Other pursuits are also limited in that process, including their right to bear arms, and their right to participate in government.
Once again, the feds are depriving someone of their rights upon a STATE conviction - and, in some cases, by passing a law YEARS after that person was convicted and released, which is in effect an ex post facto situation.
Let's look at it another way - let's say the feds pass a law that allows the FBI to come and tow away your car after you've been convicted of a DUI or of speeding in excess of 30 mph over the speed limit by a state or local court - or even if you were convicted of a DUI years before the law was passed. No due process, no hearing, the tow truck just shows up in your driveway one morning and your car is gone. Would you be so supportive of such a law? Because that is exactly what is happening here.