A disturbing amount of flute pedagogical literature includes drawings or descriptions of what types of lips are good for flute playing and what types aren’t. Usually the lips deemed flute-appropriate are perfectly symmetrical and not too thin, not too wide. I tend to think that those kinds of distinctions are garbage, as are the descriptions of the “right” lips for clarinet or oboe playing or the suggestion that students with natural overbites are born bassoonists.
I also object to the instrument-assigning days that I understand happen in many beginning band programs, at which students are allowed to try several instruments, and assigned based on the “aptitude” that they show in their first 30 seconds holding the instrument.
I would consider physical factors only when they are unusually significant. Potential beginners with genuine lip deformities might run up against challenges—or maybe not.
I worked briefly with a beginning flutist who was missing two fingers. He won’t be able to tackle serious flute literature (or even a full chromatic scale) without some kind of special accommodations—perhaps a customized instrument, or at least a unique approach to fingering—but his desire to play is strong enough that he’s willing to give it a shot. (When I left the teaching institution, he continued lessons with another teacher.)
That’s an extreme case that I’ll concede calls for a serious heart-to-heart with the potential beginner, and might be beyond a harried school band director’s ability to deal with. But to turn away a prospective student because their lips are the wrong thickness seems a little silly in comparison.
Larry Krantz hosts some interesting flute embouchure photos on his website, which are illustrative of the very personal and individual nature of flute embouchures.