This is a "classic" hyper-Calvinism statement. That is what was being taught, for example, at the Protestant Reformed Seminary in the early '80s. I have no reason to believe that things have changed since then. "Only the elect have the warrant/right
to believe" is totally unbiblical. Everyone, without exception has the warrant/right to believe. And, equally biblical is that only the elect have the ability to believe.
The biggest caveat and unsurmountable problem with the doctrine of "only the elect have the warrant to believe" is how can a spiritually DEAD sinner discern that they are one of the elect? Even true believers at times have difficulty with that kind of assurance. The fact is, only God knows who are the elect since He predestined them and elected them to Christ in eternity. There is no biblical evidence that guarantees any human being can infallibly know who the elect are. The Gospel is promiscuous. No one is exempt from the proclamation of the Gospel, because it is the Spirit working through
it that the elect are called to faith as they are regenerated and given the desire and ability to repent and believe.