Watched this movie last night and the message that it left me with is that girls should give up their careers, however promising, to be with their boyfriends even if all they want to do is sit on the beach and write songs.
I just hope Chiles is happy with her choice when her boyfriend inevitably leaves her for someone else.
I agree with the other posters that the message you described is not in this particular movie.
(1) Beau's suggestion to Chiles was not to "give up her career...to be with their boyfriends even if all they want to do is sit on the beach and write songs." His suggestion was to come with him to California, take time to write good songs (instead of settling for the lesser songs she was being offered by the studio just to take the easy path to quick fame), get experience singing those songs for the local Saturday night crowd and then go back and record an album of HER songs instead of the studio ones. He flat out told her that he thought she had more talent for writing than the studio machine and that she shouldn't sell herself short by taking theirs just because they were ready right now when she could spend that year writing her own and then put those songs on an album.
Basically he was telling her to nurture her career and pace herself because he believed in her talent, not to ditch her career for playtime on the beach with him.
(2) There is also nothing to suggest that he would "inevitably leave her for someone else." It's possible you're just projecting that onto the movie when it isn't there.
At any rate, you're welcome to your opinion but that wasn't the message I got from this film and my guess is that it isn't the message the filmmakers were trying to impart.
Even if that WAS the message of this movie I think it's a better one than the message Sex and the city series sends out to girls and women.
I'm a woman and I thought Country stronger was refreshing and much "healthier" than many movies made these days.