Idiom for being stubborn about an opinion

"He/she dug his heels in"

is often used to convey a specific act of stubbornness or defiance.

Or, if it is specific to the fact the person seems unwilling to hear what you are saying:

"I tried to explain to them, but they are just tone deaf to my ideas"

(they are not really deaf; it is just a metaphorical way of saying that they refuse to listen).

Stubborn as a mule and obstinate as a mule may convey the idea:

• Cliché very stubborn. (*Also: as ~.) I tried to convince Jake to go to the doctor, but he's as stubborn as a mule. For four years, Henry pestered his parents to let him learn the trumpet. They tried to talk him into some other, quieter instrument, but he was stubborn as a mule, and now he has a trumpet.