So, this average Japanese man gets summoned by the Demon King for diplomacy, as stated by the title. He had trouble trying to convince those powerful races to join his force, so he recruited said man for this job. The demon king assigns him a sexy demon lady, but she despises him for being weak. Later respects him for mc's convincing ability, and the two, after a few chapters had a fight and reconciled after learning and respecting each other's culture. The mc's first mission is to convince the minotaur race, and he successfully does so after finding out what they actually need a grass bed for sleep, and their requirements are quite easy.
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This is Headhunted to Another World: From Salaryman to Big Four!. It is licensed by Seven Seas
Uchimura Dennosuke is just an ordinary Japanese salaryman, until he’s sent to work in Vietnam where he dies in a hit-and-run accident. Uchimura is reincarnated and summoned to another world by the Demon King, who offers him a new job–as one of the Four Heavenly Kings of his army! Uchimura is faced with an offer he can’t refuse, but can he do the job?
The synopsis covers much of the details; the protagonist is an average Japanese salaryman and is summoned to another world due to his (overlooked in his prior life) accomplishments.
The minotaur negotiations are in the third chapter, titled "How did he capture the heart of the minotaur?". As mentioned in the question, the key is hay - the bulky minotaurs can't sleep on regular beds without breaking them, but their dialect makes communication difficult. The protagonist was able to sort this out and earn their allegiance.