Well lets take these two passages and have a look (your text):

Romans 16:17-18 (ASV)

"Now I beseech you, brethren..."
brethren=church memebers. Folks who are Christians. Now the command: "...mark them that are causing the divisions and occasions of stumbling, contrary to the doctrine which ye learned..."
Troublemakers, false teachers, people who, by their lives, declare that they don't believe what they've been taught in Sunday School. Keep your eye on them because they up to no good. What are we to do with them?
"...and turn away from them."
Mark them and turn away from them because they're trouble. I know a few like this each Sunday sharing the gossip new and old and stirring up trouble. Are they saved? Are they not? Who knows. But we can make a good guess by their actions and firm it up by talking with them about their behavior. The problem in the church is that these folks are rarely, if ever, marked and turned away from--they are tolerated.

"For they that are such serve not our Lord Christ, but their own belly; and by their smooth and fair speech they beguile the hearts of the innocent." These are definitely the kind of folks you don't want around new believers or kids.

Christians, supposedly, churchmembers who aren't acting like them. Mark them and turn away from them.

And the second passage:2 Thessalonians 3:14-15 (ASV) "And if any man obeyeth not our word by this epistle, note that man, that ye have no company with him," This is about the same as the above to this point where where it tells us why we are to turn away from or avoid them. "...to the end that he may be ashamed. And [yet] count him not as an enemy, but admonish him as a brother." Most translations use warn or admonish him "as a brother." We are encouraged not to dispose of him like a snotty tissue but admonish him gently as you would a stained handkerchief. Theres hope it(he) might come clean and thereby be of some use again.

At no point is there any reference to unchurched people. Note that I didn't say unsaved--and this is where it gets a bit hazy--just unchurched. It seems that this is a mechanism whereby lost church members are allowed an opportunity to be disciplined by the world so that they might come finally to the Lord. (General Election?) And to allow the church to sift out those who are not saved and probably never will be.


Josh
"...the word of God is not bound."--2 Timothy 2:9