Historically in the United States this question is interesting. Prior to the 1920s audiences expected to see/hear a mix of music both from the so-called high and low arts. A typical vaudeville show might have a magician, an opera singer, a Jazz band, then a pianist playing Chopin, slapstick comedians, etc.I don't have to convince anyone. Note the question mark in my opening sentence.
The two statements are crude summaries of what I have seen expressed in longer form at TC. They represent the view that classical music - usually of the CPT tradition - is of superior quality and that quality must not be debased lest the superiority of the poster be debased. It's not actually a widely held view, but it has been expressed often enough over time at TC for it to be recognisable as elitist.
As for the "film music is/isn't classical" debate, let's leave that for other threads; there's been enough of them.
But attitudes began to change to the point that a composer like Vernon Duke used that name for his Broadway songs and Vladimir Dukelsky for his Classical concert pieces, he wrote along side the others. This has been the case for decades, but opinions are softening again, and have been for a few decades, since the end of the 20th century.
Stephen Sondheim was asked about this question concerning some of his shows, Sweeney Todd, e.g. He said it was an opera when performed in front of an opera audience in an opera house but a musical when performed on Broadway. IOW, the genre was not decided on the content but the venue and audience expectations.
I tend to agree that a work is Classical when it is performed in a Classical music setting and not when it is in a film. If the film music is arranged into a concert suite or adapted into a concertante work and performed by a symphony orchestra it is Classical music - but the same music as it appeared in a movie was made up of musical cues, some lasting a few seconds, others a few minutes, and are not written as one long form work.