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.

Definitions of stubborn

adj tenaciously unwilling or marked by tenacious unwillingness to yield

obstinate, unregenerate
inflexible, sturdy, uncompromising
not making concessions
not obeying or complying with commands of those in authority
bloody-minded, cantankerous
stubbornly obstructive and unwilling to cooperate
bolshy, stroppy
bullet-headed, bullheaded, pigheaded
obstinate and stupid
dogged, dour, persistent, pertinacious, tenacious, unyielding
stubbornly unyielding
contrarious, cross-grained
difficult to deal with
devoting full strength and concentrated attention to
hardheaded, mulish
unreasonably rigid in the face of argument or entreaty or attack
haughtily stubborn
strong-minded, strong-willed
having a determined will
not tractable; difficult to manage or mold
willing to be taught or led or supervised or directed
dutifully complying with the commands or instructions of those in authority
meek, tame
very docile
sheepish, sheeplike
like or suggestive of a sheep in docility or stupidity or meekness or timidity
inclined to yield to argument or influence or control
manipulable, tractable
easily managed (controlled or taught or molded)
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adj not responding to treatment

“a stubborn infection”
stubborn rust stains”
not tractable; difficult to manage or mold

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