Well, sure, the Beatles are not "traditional" folk music, at least not according to one well-established definition ~ obviously. If you define "folk music" according to one of the more inclusive defintions, on the other hand, they might well qualify.

Any artist will create works within the genre/style in which he/she performs. Someone who sings unaccompanied British ballads with unknown long-past origins will undoubtedly write songs that sound consistent with that tradition (if he indeed finds it meaningful to write any new music at all). Someone who plays trad-jazz clarinet will, if he composes anything, probably produce work that sounds 75-100 years old.

There is not "a" tradition, there are many many musical traditions, and each has its devotees.

I do have a problem with the school of thought that argues that their particular favorite style is somehow sacrosanct and inherently superior to others; this usually has something to do with a reverence for truly OLD material.

Some of us need to be reminded that NO ONE KNOWS WHAT ANY MUSIC SOUNDED LIKE PRIOR TO THE DAWN OF RECORDING TECHNOLOGY. Music is always performed in the present moment, and is always contemporary, the product of the living person(s) creating it out of (and into) thin air. Too often, folks who feel such a great reverence for a style of music that they believe has roots in the deep past are really just trying to perpetuate sounds that occurred early in the era of recording technology ~ in other words, the moment in time that they are trying to freeze really dates back no further than about 1925.

Hey, everyone is certainly entitled to like whatever they like, but let's please keep some perspective about this.