"Therefore come out from them and be separate, says the Lord. Touch no unclean thing,and I will receive you." ~ 2 Corinthians 6:17
"I urge you, brothers, to watch out for those who cause divisions and put obstacles in your way that are contrary to the teaching you have learned. Keep away from them. For such people are not serving our Lord Christ, but their own appetites. By smooth talk and flattery they deceive the minds of naive people. Everyone has heard about your obedience, so I am full of joy over you; but I want you to be wise about what is good, and innocent about what is evil." ~ Romans 16:17-19
There is no doctrine of distinctiveness in the Bible.
Not as it has been taught in my fellowship, anyway; there's no scriptural doctrine of distinctiveness that says "We have everything right and any other believer or church which doesn't is apostate and we must have nothing to do with them," and then quotes verses like those above.
Because in the first one, Paul is talking about unbelievers. Not people who believe in Jesus Christ, Son of God, Savior, crucified and risen and reigning, but disagree with you about some spin you've put on scripture. Unbelievers. He's talking about people who don't believe at all.
The second one is talking about people who are trying to split off and divide and "disfellowship" (another word which - like "distinctiveness" - is not in the Bible). After all, it's the person who draws lines where God hasn't that is divisive; not the one who, perhaps unwittingly, crosses that wholly imaginary line. So to use that scripture as a proof text to justify divisiveness would require one to not associate with himself or herself.
Good luck with that. Sounds kind of schizoid to me.
Distinctiveness from unbelievers, yes. I can see that. (If you have to put an extra-scriptural label on it.) We should be displaying the mind and heart and Spirit and actions of Christ, which will be difficult for unbelievers who do not know or will not accept Him. We do so to win their minds, their hearts, their souls, and their actions to Christ. We do so because we can; because as believers we have the Spirit of Christ. (Romans 8:9-11; Ephesians 1:13).
But not distinctiveness from other believers, even those with whom we disagree - no. Decidedly, NO. Insisting on such "distinctiveness" is not displaying the mind and heart and spirit and actions of Jesus. (And, no, we do not accept as fellow-believers those who live such lives sans shame or confession that they effectively deny a profession of faith in the humanity and divinity of Jesus Christ [Jude 1:4; 1 Corinthians 5:9-11; 1 John 2:18-23].)
Scripture has a word for teaching men's rules as if they were God's, and it is not "distinctiveness" ... it is "vain." (Matthew 15:9; Mark 7:7).
Let's just face facts.
The kind of distinctiveness that separates believers based on the teachings of man but not God is just a way to justify saying, "I'm right and you're wrong. I'm saved and you're not. I'm better than you are." It is arrogance. It is the refuse of male bovines. It is a lie.
You want to know what the truth is, what scripture does say, and what a great equalizer it is - not only of Jews and Gentiles but everyone on any side of any question?
"There is no one righteous, not even one; there is no one who understands, no one who seeks God. ... Righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus." ~ Romans 3:10, 22-24
None of us has it all right. None of us has done it all right. Not me. Not you. Not anyone. All of us are toast, as far as righteousness goes, but for the grace of God through the sacrifice of Christ.
Now that is doctrine. And we would do well to heed and teach it.
We would do even better to also trust God and not to lean on our own understanding (Proverbs 3:5).
That's doctrine, too.