"I Hate You" was a punk rock song which was known on planet Earth in its year 1986. A rider on a San Francisco bus was playing this song at an excessive volume on his ghetto blaster when he was neck-pinched by Spock, a Vulcan time-traveler from the 23rd century, attempting to control the decibel level the bus' passengers were experiencing. The passengers were grateful. (Star Trek IV: The Voyage Home)
We're all bloody worthless,...
According to the movie credits, the song was performed by the obscure band Edge of Etiquette. (Edge of Etiquette was, indeed, so obscure that it is rather difficult to find anything more about them than their having performed this particular song.) The punk on the bus who flipped Kirk "the bird" was played by Star Trek IV associate producer Kirk Thatcher. According to the Star Trek Encyclopedia (4th ed., vol. 1, p. 354), Edge of Etiquette was a pseudonym for Thatcher.
The lyrics were also written by Kirk Thatcher, and arranged by Mark Mangini. A game card, from the Star Trek Customizable Card Game released by Decipher, excerpted the lyrics of the song. Thatcher had complained that the new wave music previously considered would not have been an accurate representation of what a 1980s punk would listen to, and offered to write "I Hate You" instead.
The song was also heard in the 1987 Frankie Avalon/Annette Funicello beach party comedy Back to the Beach.
Edge of Etiquette
The reason for the obscurity of Edge of Etiquette is the band not having existed longer than approximately one and a half days after the movie had gone into post-production. Thatcher provided the vocals as well as the lyrics for the song. The rest of the team consisted of several such members of the sound department as Mark Mangini, who converted the tune Thatcher had in mind for the song to something that could be played.
To achieve an "authentic" gritty punk sound, Thatcher, Mangini and company moved into the hallway of the sound studio where the post-production sound work was being done in order to record the song. They also used the lowest quality microphones and instruments they had available to enhance the illusion that the song had been recorded live at a punk club.
This was the only time Edge of Etiquette ever recorded anything or played anywhere. No royalties or licensing fees of any kind were ever paid to anyone for the use of the song "I Hate You" in Star Trek IV. Thatcher did get some royalties when the song was later used in the movie Back to the Beach, but the song was not included on the film's soundtrack album.  The song remained unavailable for purchase until the soundtrack was re-released in late December 2011.