That was never illegal to begin with, in the US.

It wasn't, but it was my understanding that that self-policing was in effect because they didn't want the law to exist.

Now that the law -can't- exist, will the self-policing continue?

Initially, movies were not protected by U.S. free speech laws, but they've (generally) been protected since the 1950s[1]. So today's opinion may not change things meaningfully (I haven't read it yet).

There is likely good business incentive to keep the policy. If parents can be confident their children will be barred from movies they'd want to forbid, they'll be more likely to send them to the theater, give them cash to see movies, etc. The MPAA probably gathers enough data & does enough market research to have some sense of whether or not this outweighs the increased revenue from teenagers seeing more adult fare.

[1] Brief history: http://www.lehigh.edu/~infirst/moviecensorship.html

I thought kids couldn't see R-rated movies in theaters without parent supervision.

I remember being turned away from a ticket counter for that.

I'm sure someone will correct me if I'm wrong, but I'm fairly sure you legally can watch an R-rated movie, it's just the policy of the theater that you don't.

This is correct. This is also the reason why you would be hard pressed to find a venue that would show an NC-17 rated title in some places since most major theater chains refuse to show NC-17 rated films as policy.

Voluntary self-regulation by the film industry. The MPAA is to movies what the CCA used to be to comic books.