In Nichelle Nichols' autobiography she talks about how the network insisted the scene be filmed both with and without the kiss, and of course, being good loyal actors, they complied. But, on takes without the kiss, something always seemed to go wrong… Shatner flubbed a line, the boom was in the shot, the cameras weren't quite set up correctly… eventually they ran out of time and were forced, "reluctantly", to submit only the takes with the kiss. I recommend Beyond Uhura. Also Kate Mulgrew's "autobiography" of Captain Janeway is a great read too. :)

And then, just as now, many said “I wouldn’t have a problem with it if they weren’t rubbing it in my face!”

*American television. IIRC British television had an interracial kiss over a decade earlier.