He's a hybrid with pointed ears, a tall lean body and a calm detached exterior. Guess who?
Elrond Halfelven. Everybody says Spock.
Now that the mind games are out of the way onto human non human hybrids! Spock opened the floodgates. everyone in SF or fantasy seems to be preoccupied with the most mixed of all mixed relationships. The author went through a period where he longed for a cool Andorian girlfriend (the hot ones are too violent.) Anything goes in fantasy but can we have realistic alien/human hybrids in science fiction?
Short answer: NO.
A human and alien in a relationship will probably be lucky if they don't poison each other by kissing (or other activities). Humanoid life seems incredibly unlikely in itself so alien human relationships may be limited to humans who find shapeless purple masses attractive. I'm sure there are some people like that out there and I don't want to know.
But assuming there are humanoids out there in the big universe it might be a big stretch to have them eat the same foods as humans. Giving your love, that shy lass from Leonis Prime a box of chocolates for Valentine's day may be fatal. Sending flowers might trigger anaphylaxis shock. Swapping spit might make her fur fall out. You get the idea. Long distance relationships are hard.
Assuming you can enjoy some of the same foods (maybe some carbs if you guys aren't watching your figures.) could be handwaved. What the hell good are strange new worlds if the foodies have no new munchies? Truly compatible ecosystems are often assumed in SF like ftl drives.
That doesn't mean you can breed. I have my official killjoy hat on now. The weight of evidence is with me. Humans can only breed with humans despite those humanzee hybrids the Soviets were claiming. Now when you are talking human/simian hybrids you're talking species that share 99.5% identical genetic codes. Odds are any aliens are not even that compatible with us or vice versa.
What about Precursor seeding of life forms? The Precursors ran around mucking with any number of worlds. Some settings have them seeding microbial life on lifeless planets implying we all have a common origin.
First of all having a common microbial ancestor doesn't mean you can breed. We share common single cell ancestors with every form of life on Earth of you go back far enough. Try having sex with a redwood and see what it gets you other than locked up. Maybe the intervention occurred sooner than that or at regular intervals. The Precursors made sure all these planets had compatible life forms down to the dominant species looking alike, sharing pheromones and wanting to get busy. Again they'd have to be very similar genetically to us and that would require a lot of intervention. How long ago did this intervention stop? Is it the reason those Grays want our women and men?
Maybe the Precursors dropped human stock off on other worlds and they evolved somewhat differently (what the heck is wrong with your forehead?) Well then we aren't talking aliens anymore, are we? Note I'm not even dealing with genetic engineering making children possible because this post is about hybrids. Those are chimerae or floor models depending on your degree of enlightenment.
I can't be a complete buzz kill though, can I? I usually turn these kind of things around and point ways to ensure mayhem.
Perhaps the Precursors had a plan, in humans or the race of your choice (I like fox people myself.) Perhaps they encoded a 'black box' sequence that allowed them to breed with other humanoids. Let's throw in some universal pheromones while we're at it. The goal is to eventually meld all the most successful characteristics of their carefully monitored offspring into a single god like race. Then they'd have someone to talk to!
The hybridizing race would have an enormous advantage. They could mate with species with greater environmental tolerances than them and colonize more worlds. They could breed selectively to gain others' strengths. You might have to get the psionic humanoids with the attitude drunk first but I digress. Other races might view them as a deadly threat to their own futures or jump on the bandwagon. this could lead to a galactic civilization or a galactic war as the possibilities for 'exchange' increase worse than the discovery of the Babel Fish.