Use the adjective stubborn to describe someone who is not open to new ideas or ways of doing things, like your uncle who refuses to listen to any music made after 1990. Stubborn is the opposite of flexible.
The Middle English version of stubborn carried the sense of “untamable, implacable,” and there’s still a hint of that in how it is used today. A stubborn person holds on to a view or an attitude, refusing to change — to the point of being unreasonable. Things can also be stubborn, like a stain that no amount of scrubbing can clean or a medical condition that, even with treatment, doesn't improve.