Let us say that he keeps bringing the subject up, badgering you:
You might point out that his badgering is not Biblical, either. Brothers are to be corrected in private, then with witnesses, then before the church, and then be done with it. As for non-believers, if they won’t hear you, you leave them be until they come around on their own. If you have to find him the passage where the Lord instructed the 72 to shake the dust from their feet if a town wouldn’t hear them, rather than hanging around badgering the people into compliance to the faith, then do that. He won’t find a Biblical example of an early Christian pestering people is such a manner as he is doing.
If you are not being badgered, then steer clear of the subject, unless you honestly don’t think he knows that the Church teaches that the grace of his salvation pours into him through Her alone, whether he knows it or not…for we do still teach that there is no salvation outside the Church, even though we are willing to admit that the Holy Spirit will blow where He wills and may use the graces poured upon us as He chooses. If you do not think he knows, you may sit down with him and say, “Jack, I’ve been listening to your preaching to me, and I’ve been convicted…of not preaching the truth to you. So let me tell you about the Catholic Church.”
Whatever the case, if you keep getting his preaching after that, you might tell him that you will pray ardently that he will be given the wisdom in this life to be docile to the Holy Spirit in all things, and eternal life in the next, and ask that he do the same for you. Tell him he may feel safe that he has done his part to warn you of the danger he thinks you are putting yourself in, that you hope you have done the same for him, as he is conscience-bound to join the Catholic Church once he sees the truth of it, and so it is time that you both leave the subject alone.
Then do it. When he brings the subject up, just say, “We’ve been through this. You’re in my prayers, Jack. I trust I’m still in yours. If so, you’ve done your part. Let’s just shake the dust of each other’s towns off of our feet and just have some peace.” Then tune him out until the subject changes. Act as if he is not even talking to you.
Repeat, repeat, repeat.