They don't reject it. They see it differently than you do. The difference is not a rejection. Instead, they focus on a narrow definition of the parties to the covenant. Historically this traces from a narrow set of 18th and 19th Century Anglican Clergy and German Evangelicals.
They teach that all Christians benefit from the Covenant.
Are they right? Sigh. Many think not. Does it disqualify them as Christians? Christianity has been very diverse since Paul's day. God will determine who and what he accepts. That's not up to us. We are responsible, however, for what we believe and teach.
Presuming that Witness definition of the New Covenant is not what Paul taught is insufficient. If we're going to argue it out with Witnesses we must present proof, not merely citing Galatians. They, of course, could cite those verses and apply them to you.