I see it as considerably evolved but still undeniably classical music. By this time many musical composers were using 20th Century popular music styles in their music - not just Gershwin, but also Holst, Rachmaninoff, Shostakovich, Copland, and of course Debussy - almost to the point that they were redefining the role of classical music in the musical landscape of the early to mid 20th Century, in the process acknowledging emerging pop music such as jazz, blues, swing, etc. I mean, there are some who consider Gershwin's "Porgy and Bess" and Bernstein's "West Side Story" as classical music pieces in their own right.
The 20th Century era of classical music was very much an exciting spectrum within the extremes of "popular" classical music that can still carry a decent tune and maintain a variation of the tried-and-tested sonata form, right up to the experimentalists like Cage, Stockhausen, etc. all trying to stretch the limits of classical music and take it to new ground, pushing it forward.
By this time, film was also gathering popularity, and several famous compsers were making music specifically for this new medium, such as Malcolm Arnold, Bernard Hermann, etc. The classical music changed to fit in with these styles including the increasing American influence on world culture, so it's no wonder people consider such classical music as a form of jazz.
Although to be honest classical musical composers have been using popular melodies of their time in their songs for a long time, be it traditional songs or even other composers' works (Brahms using Haydn, Rachmaninoff using Paganini, etc.). No different to pop music incorporating Latino, Bollywood, South American, African, and of course classical influences into their works today.