In regard to Romans 2:13, we need to examine this verse in CONTEXT. Paul was talking to the Jews (continue reading on in Romans 2:17-24) about their judging of the Gentiles and then points them to their own law (standard of judgment) and hypocrisy and tells them that the doers of the law will be justified before God (verse 13). That leaves them out, along with everyone else. (Romans 3:22-28; Galatians 2:16)
The standard they wanted to measure up to was the law. Paul was telling them that the doers of the law will be justified. So, obey the law, obey all of it, but if you don’t obey all of it, you have failed! He tells them that the Gentiles who didn't have the law according to the knowledge of the Jews were instinctively doing the things of the law (verse 14) and will be judged accordingly. How much more so the Jews? Paul was showing the self-righteous Jews who judged the Gentiles that they were not able to measure up to the perfect standard of the law. They were hypocrites.
This is why Paul tells us in the very next chapter in Romans 3:28 that we are justified by faith apart from the works of the law. No one was able to perfectly obey the law except for Jesus Christ. If you fail even once (stumble in one point), then you become guilty of all.
In James 2:10, we read - "For whoever keeps the whole law and yet stumbles in one point, he has become guilty of all." In Galatians 3:10, we read - "For as many as are of the works of the law are under a curse; for it is written, "cursed is everyone who does not abide by all things written in the book of the law, to perform them."
The Jews could only be justified before God by keeping the Law, but he or she has to be 100% perfect, which is impossible. A person can’t fail even once, not ever. But all have failed (Romans 3:23; 6:23) and that is why man is justified before God by faith and not by works of the law. (Philippians 3:9)