It's unlikely Richard I was gay. He was known for being exceptionally cruel, and although he spent one night sharing a bed with Philip II as a sign of unity, no one at the time thought anything of it.

He had at least one illegitimate child and held off on marriage because he was having an affair with a woman he couldn't have married for political reasons. Richard I spent much of his life putting down rebellions and going on crusade, it any of his contemporaries thought he was gay they would have made that accusation.

There's a mention to him committing a sin like in Sodom and Gomorrah, but it's thought to reference the fact that he would crush his enemies and rape their women.