As for the die hard science lovers out there who say its impossible, this in in a universe where we can travel faster than light and where a device can disassemble a person send them through a stream of energy and reassemble them in less than 10 seconds.
The "fi" part of sci-fi is there for a reason
Heh - but I like my Fi to have some internal logic. They worked quite hard to give warp drive and transporters a great deal of in-universe science to explain them (even if they keep accidentally contradicting themselves on the fine print). Inter-species breeding is very poorly thought out compared to that.
The fact that humanoid life forms are a massive genetic experiment by Trek's own 'First Ones' was a nice step in the right direction but it just doesn't go far enough to explain how beings with vastly differing genes and wholly different blood chemistry can interbreed naturally.