It was mentioned in the Voyager episode The Disease. People made a big deal out of that at the time but I just assumed it was because it was a NEW species. Starfleet has to find out if there are things that can make us or them sick or cause some kind of great galactic incident. Ensign Kim caught a space STD.
They also went on about Spock being half Vulcan, what Kirk and Riker got up to, Paris marrying a half Klingon, Worf and Jadiza...I'm sure I've left someone out. Those rules might well have come about BECAUSE of Kirk...
We should also mention that Crusher had a relationship with a Trill and of course Deanna was the product of a Betazoid/Human pairing. Did she also have a relationship with a new species as well? I can't remember.
As far as Paris/Torres and Worf/Jadiza they were all species who were members of the Federation. Everything about them was probably well known. You married a Klingon at your own risk of course.