Depite the production gaff of having a Klingon representative with a UFP symbol on the viewscreen
A sign that this particular Klingon is the one tasked with the humiliation of interacting with the Federation? His ship is
a purposely sent prisoner transport...
"Heart of Glory" definitely gives the impression that the average UFP citizen or even the average Starfleet employee is unlikely to ever see a single live Klingon, let alone be confronted by a pair of them. And that apparently goes for Worf as well! TNG "prehistory" seems to concur, as the Empire never came to reclaim Worf or anything like that.
Certainly it seems that if there ever were joint maneuvers between UFP and Klingon military forces, those were isolated incidents like "The Time Trap", and both sides kept their mouths shut afterwards. Cultural exchange would probably be about as extensive as between North Korea and the United States: whatever was exchanged would have been dismissed as meaningless propaganda on both sides.
I don't think any of the TNG era shows really contradict this take. Sure, we learn of "exchange students" of various sorts, and even a few Klingon-Human hybrids, but those may be rare exceptions or (save for K'Ehleyr and B'Elanna Torres) post-2364 developments.