While we are initially and ultimately saved by God's grace, this does not mean we can live however we like (and or sin and still be saved). God's grace is always followed by obedience. If not, then what separates the believer from the unbeliever? A belief alone? Does a belief alone really make someone a better person? There are many warnings in the Bible about having a belief alone with no works. James says faith without works is dead (James 2:17). Jesus says why do you call me Lord, Lord if you do not do what I say? (Luke 6:46). Jesus says if you will enter into life, keep my commandments (Matthew 19:17). Even believing in Jesus is a commandment or Law (See 1 John 3:23). The Bible talks about what happens to those who are lawless. If one is against Law they are against GOD. For the law is not made for a righteous man (i.e. somebody who obeys's God's laws). God's laws are made for those who are disobedient, ungodly, or sinners, etc.
"Knowing this, that the law is not made for a righteous man, but for the lawless and disobedient, for the ungodly and for sinners, for unholy and profane, for murderers of fathers and murderers of mothers, for manslayers," (1 Timothy 1:9).
Important:
The confusion arises on this issue is because people look to Paul condemning believers in following the Old Law as a means of justification alone without God's grace. For one, we are not under the Law given to Moses (Which was for Israel). Scripture says the Law has changed (Hebrews 7:12). So God's laws have not been eliminated; They merely have changed between the Old Covenant and the New Covenant. Two, we are initially and ultimately saved by God's grace. So Paul was condemning trying to be justified without God's grace by a system of works or law alone. This does not mean we are not justified by works. James even says point blank that we are justified by works.
"Ye see then how that by works a man is justified, and not by faith only." (James 2:24).
But what about Ephesians 2:8-9 and Titus 3:5?
Both of those pieces of Scripture are talking about "Initial Salvation" and or "Ultimate Salvation." Ephesians 2:1 says Christ quickened us which is a one time event. Titus 3:5 talks about how we are renewed and regenerated by the Holy Ghost. This is talking about being born again spiritually which is also a one time event.
As for Judging other believers:
Not sure why you think that we cannot judge other believers. Jesus said judge righteously (See John 7:24). Paul says reprove the unfruitful works of darkness (See Ephesians 5:11). Paul also says Scripture is profitable for reproof, correction, etc (See 2 Timothy 3:16-17). There are even steps to properly correcting (judging) a brother who has wronged you (Matthew 18:15-17). So no. The idea that we cannot judge at all is unbiblical and even silly. For do you not think that certain sins are wrong in this world? By saying that certain sins are wrong you are in fact judging (because somebody out there is doing those kinds of sins). Granted, I do not think we should not forever condemn people (unless they committed an unforgivable sin) because there is still a new day whereby they can repent. In other words, we should focus on attacking the sin and not the person when we judge.