The points Emerson makes in "Self-Reliance" are all closely connected. If you accept the broad theme of the essay, that it is vital to be yourself rather than attempting to imitate others, then you will probably agree with most of the ideas he expresses. Take the passage at the beginning of the second paragraph, where Emerson sets out what he means by self-reliance:
There is a time in every man's education when he arrives at the conviction that envy is ignorance; that imitation is suicide, that he must take himself for better, for worse, as his portion; that though the wide universe is full of good, no kernel of nourishing corn can come to him but through his toil bestowed on that plot of ground which is given to him to till. The power which resides in him is new in nature, and none but he knows what that is which he can do, nor does he know until he has tried.
The ideas expressed here are always relevant, but you can certainly argue that they have particular force in the light of contemporary celebrity culture. The media, including advertising and social media, continually invite you to compare yourself to others, measuring your accomplishments, your wealth, and your physical appearance against standards that are unattainable for most. The effect is to make many people feel like failures. Emerson sees only one reasonable standard of comparison: to compare what you are with what you are capable of being. Envy is ignorance; if you knew everything about another person's life, you would not envy them. Imitation is suicide because by trying to be someone else, you kill who you are and who you are capable of being. The most inspiring aspect of this idea is that you have within you a power that is "new in nature." If you do not develop your own personality and talents, they will be lost to the world. This is a valuable antidote to a culture built on imitation and aspiration.