Will "believers" or, more precisely, "the righteous in Christ" be judged? The answer is no; not with respect to their salvation. And what is salvation? Spiritual rescue from the consequences of sin; to be saved from eternal damnation.
Make no mistake about it. We are justified by faith in Jesus Christ. The Bible says it; I believe it; that settles it.
My statement of faith is described in the article entitled "Justification By Faith." A short synopsis: "Only the act of justification by faith in Christ can save a man's soul. That is the righteousness bestowed by God through faith in Christ by whom a sinner is freed from the penalty due for his sins."
The Apostle Paul says:
"I may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith."
According to civil law, if a man is convicted of a crime, he is sentenced by the courts to pay a debt to society. That could result in a prison term or even capital punishment. In much the same way, according to God's Law, a sinner owes a debt to God because of his sins.
And again, the Apostle Paul says:
"For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord."
And once again:
"He has cancelled out the certificate of debt consisting of decrees against us and which was hostile to us; and He has taken it out of the way, having nailed it to the cross."
And let's not forget the Apostle John:
"He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God."
Now believers will stand before the judgement seat (2 Corinthians 5:10) and some have said that their works will be judged. However, the word "judge" can be confusing, especially to babes in Christ. More correctly, their works will be "put to the proof." The NAS uses the word "test," the KJ the word "try," and the Douay the word "assay" and this is by fire. The Apostle Paul gives a vivid description in 1 Corinthians 3:12-15:
"The fire itself will test the quality of each man's work. If any man's work which he has built upon the foundation remains, he shall receive a reward. If any man's work is burned up, he shall suffer loss; but he himself shall be saved, yet so as through fire."