This is true if you're a dispensationalist. This is *not* true if you're *not* a dispensationalist. There are many Christians who are not.
In my opinion, all one has to do is read Scripture. The New Testament is abundantly clear that God's reaction (and interaction) with humanity was different with Adam, Noah, and Moses - and that in this present age since the crucifixion and resurrection of Christ, we are in a unique age of Grace.
Dispensationalism is a big word that I doubt even most Christians understand or even care to research. But if you are a believer in Christ, you understand it through the discernment of the Holy Spirit. There is so much evidence of Scripture of it's core tenants that I really don't understand how someone can call themselves a Christian, read the verses outlined and explained in the link below, and reject it.
DISPENSATIONALISM CATEGORIZED SCRIPTURE LIST by Nathan Pitchford
If it is true, it certainly does not depend on man’s doctrines or categorizations one way or the other. Truth stands apart from man’s winds of doctrines that carries about and tosses to and fro.