The world is full of insincere people...so that means there will be insincere christians as well. God's knows who will be His. If calvinist's beliefs are correct when they say God chooses people ahead of time to be saved, and some not to be, then that means "no one" knows if they are a true, born-again christian. There is no permanent label to tell one from another...because we know calvinists fail just the same as everyone else does.
If a person says they have accepted Christ, then that is where their heart should be. I cling to the promises that God has made to me. I do not doubt that I am saved. I do not believe He picked me as special from among the people. The gift of faith that God gave me is strong enough to believe that I will endure to the end by His power.