I think you mean the following story:
Subjugation by James Galloway (Fel).
Every detail of your question matches
- The story contains elf-like blue aliens:
The Faey representative, a high-ranking military officer, was a breathtakingly lovely human-looking female with light blue skin and pointed ears.
- However they can turn purple if embarassed or angry:
... as the Faey removed her armor, then stood there, her face turning purple in a blush—red blood flushing blue skin— ...
- They conquer the earth and turn it into a farming colony:
Without firing a shot, without killing a single human being, the Faey Imperium conquered Earth. And so, Earth became a farming colony under Faey control.
- They have telepathic powers:
The Faey were a telepathic species, and they used that telepathic power to quickly move in and root out all the resistance movements that had sprung up since their arrival.
- The human protagonist has an innate talent for defending against telepathy:
Jason had a very organized and controlled mind, thanks to his father. [...] That mental training gave him the ability to control his mind, present to the world a repetivitive train of thought which the Faey couldn’t seem to penetrate without being very serious about it, an upper layer of sorts that concealed the true thoughts beneath it.
- He later also develops telephatic powers:
Learn how to block out broadcasted thought, then learn how to burrow into another’s mind for information. Learn how to defend, then learn how to attack. Jason was getting pretty good at the defense, but still had much to learn as far as attacking went.
- The protagonist finds out he has a noble alien ancestor, and uses this information to get a noble status for himself:
I’m a telepath because I have a Faey ancestor, and that Faey was Zera Karinne. [...] From what I read in the Charter, by the rights of noble birth, I can lay claim to the vacated House of Karinne by simply staking that claim in your Majesty’s presence with the ring.”
All quotes taken from Subjugation, available online