You don't hear about it much any more. Just today I realized I hadn't heard the term in years. Heck, in the sixties there was a rock band named The Rhythm Method.
That's encouraging. It makes me think at least some battles in the 'culture war' don't go on forever.
For the young and innocent, "the rhythm method" is the one method of family planning the Catholic Church has ever promoted. It involves keeping track of the wife's cycle and trying to confine sex to the times of month well away from ovulation. The joke was that people who practice the rhythm method are called parents.
I think it's a monument to their devotion that hundreds of millions of Catholics have remained loyal to their faith while deciding not to pay attention to what doctrine says about contraception. The clergy seem to have quit beating the drum on the matter; I imagine they've realized the congregation just tunes them out on that subject.
The 'fall back' position has been opposition to abortion. That's a much easier position to maintain, if only because people can't possibly get interested in having an abortion anywhere near as often as they get interested in having sex.
It's encouraging to realize that some battles in the 'culture war' do get won. You can still hear lots of arguing about abortion, but there seems to be only token lip service to opposing most kinds of contraception that actually work.