No. They are not alienating other music in favor of nostalgia or favoritism, they just enjoy their era’s music more.
It is not that they refuse to believe that music outside of their chosen era can be good, it is that they truly enjoy music from their era more.
They might listen to newer or older music, but they will not enjoy it more than their music.
There is actually historical evidence with one of the most noticeable examples backing my point is Wolfgang Amadeus Mozart's music is highly praised today and is scene as revolutionary, but he was mocked and ridiculed by critics and fans of Baroque style music across Europe.
Those that looked at Mozart's musical opera 'Die Entfuhrung aus dem Serail' would see that Mozart's music was fairly popular with those that heard it, and was only really criticized by those critics that listen to older style music. With one of the most largest critics being Antonio Salieri who refused to stray from tradition when making music, and Antonio Salieri would later praise Mozart's music more after the composer had died and receive a cult following, only then would he stop praising Mozart in private and stop gatekeeping in music.
If you still don't believe me here are some trends just from the 20th century:
Many people that enjoyed Classical music hated Blues music. Why? Because it was different and original and didn't sound like
their music.
When The Blues became normalized because of the new generation, the new generation hated Rock and Roll. Why? Because it was different and original and didn't sound like
their music.
When Rock and Roll became normalized because of the new generation, the new generation hated Pop. Why? Because it was different and original and didn't sound like
their music.
When Pop became normalized because of the new generation, the new generation hated Hip-Hop. Why? Because it was different and original and didn't sound like
their music.
It goes on and on sure these eras had some bad music, but do you know what else these eras had?
These has their: B.B King, Elvis Presley, Michael Jackson, and Dr. Dre. These eras Mozart, the people that were disliked and looked down upon by a lot of the older generation because it was different and original and didn't sound like
their music.
It is a trend throughout history that many, if not most people reject newer music in favor of older music. I am not saying its wrong to do so I am saying you're missing out on good music if you do this.