It is still an important belief in many American churches. You can find references to TULIP as an encapsulation of their beliefs in this area, and you will find some mention of it in /r/christianity. Nevertheless, I think you are right in saying that it is no longer emphasised. I'm basing that partly on never having heard a sermon on the matter over the last 40 years, attending Reformed churches in England and Scotland, but more significantly I've never come across a modern sermon or commentary mentioning predestination on international preaching resources such as Text Week - and I read rather a lot of them while procrastinating preparing my own sermons.

Any answer to your question is probably going to be subjective, but my impression is that interest has shifted away from theology over a lot of denominational spectrum, not just in the Reformed tradition. For instance I doubt that many modern Methodists would know what Arminianism is, even though it reflects a belief associated with their church; and the director of theology of one of Britain's major Catholic public schools told me that Transubstantiation is no longer something much considered in his denomination. I don't wish to imply that anyone disbelieves in these points, just that they are no longer major points of interest for the majority, where they used to be core beliefs.

Interest seems to have shifted more towards exegesis (understanding what the Bible says when taken on its own terms) and "higher criticism" (putting the texts in a historical context). Exegesis was always a Protestant concern, but the Catholic church has moved more in this direction (producing some good scholarly work such as The New Jerome). Text criticism is newer, driven by the wealth of new information from things like archaeology, ancient history of the Middle East, the Dead Sea Scrolls, computer analysis of text and so on - this is in contrast with earlier periods where the commentaries available to the average preacher were basically verse by verse explanations of what the text says.

I cannot prove that the change in exegesis and the interest in higher criticism has a causal relationship with the reduction of interest in theology, but my suspicion is that such a relationship exists, and that "getting in to the head of the writer" is seen as more interesting than tap-dancing through a theological minefield without accidentally committing heresy. (Which reminds me - I must check if I am booked for Trinity Sunday next year).