Several points:
1) Guys, we're talking about a game universe where its possible for an individual to fly from one section of space to the other by getting outside of Einstein's Cage and defying the tyranny of Light Speed and do so admirably without having to resort to generation ships or super cryostasis or a combination thereof. Our entire modern understanding of physics, the universe and everything is being chucked out the window from the word go for the sake of the game play. We can never and will never ever ever ever ever ever ever have it be possible to ever be in a situation where honest exploration of the Galaxy is ever possible ever without discovery some new SCIENCE and then having to question approximately ALL OF OUR SCIENCE all the way back to the Ur Empire, frankly, we're more likely to chuck the new science than uproot millenia of knowledge. Going faster than light in any way is like saying 'whats faster than fast?' or 'whats more horizontal than horizontal?' So keep that in mind when you try to make appeals to suspension of disbelief and realism and slapping anyone down for their wild and crazy Sci Fi ideas, theirs are just as legitimate, and frankly, likely as the premise in the first place. Take a breather.
2) Regardless of the ability to reproduce, interspecies romance is a genuinely interesting social topic but, I think, not nearly as big an impact on the gameworld as people think it would be. If you think Captain Sheparding about the place would be acceptable not only by one species but by any other species than you woefully misunderstand tribalism, or the xenos equivalent. On a practical game level, it will never reach the point where you'd need to worry about rebellions. I'm sorry, but even in real life if you persecute teh gays (for the nearest taboo equivalent), you'll never worry about teh gay rebellion, it simply isn't happening and if it does it'd be hilariously crushed. So too would the same be true of a xenos-love rebellion in the game of stellaris, it'd be an uprising so insignificent your weakest planetary governor would probably barely notice it on his day-to-day oppression and tyranny news updates. It'd only ever really be a problem in EXTREMELY cosmopolitan planets but then it'd be a question of 'how' cosmopolitan, too much diversity of genuinely incompatible species would only reinforce tribal habits present in real life human societies, with people hanging around those most similar to them. Not a healthy environment for hot green skinned alien babe lovin'. Except prostitution.
Except it does have interesting applications in terms of seduction.
Imagine you had a very talented agent, or general, or planetary governor, whats to say that a rather comely looking little thing of another, but mechanically applicable species worms their way into his good graces? I mean, sure, they'll never have a kid, but thats not your concern as Space Emperor.
You're concern as Space Emperor is the fact your planetary governor has a xenos whispering sweet, sweet, nothings into his ear at night.
And making him dream dreams you'd rather not be on his mind when he woke up the next morning.
Behold, the dawn of Space Bond.
3) Genetic modification: That a chromosome splicer in your pocket or are you just happy to see me?
4) Possibility of other species being compatible with species X: About as likely as FTL travel. Go nuts. Just make sure it fits the universe's internal logic.
5) Reproduction: Generally speaking it depends largely on how Paradox plays this. A species pulling an Asari is... relatively believable, because its arguable if they even NEEDED the genetic material of another being in the first place. But if paradox does the old 'Precursor race edited/made/engineered/Garden of Edened' younger races into being, a la Star Trek, with the pre-conceived intention that genetic strands would all produce similar dominant species on different planets eventually, then sure, go nuts. Also genetic engineering does make this possible, as does nanotechnology or, if you have the testicular fortitude to be bloody honest about it, Space Magic.
That said, I wouldn't mind it personally if it WAS possible for different species to interbreed. It would make the question hold actual moral weight in my eyes, whereas otherwise I'd just see them as hedonistic little nothings trying to justify exotic lust with situational morality.