BGG,
IMTU aliens were fairly common, but they were common in the same way furniture or scenery is common. (Robots IMTU are common too, but you're all aware of my robots as toasters opinion so robots as humanoid, bipedal, machines with a face were very rare indeed.)
I never had a group member who played an alien. I never anyone who even wanted to play an alien. All anyone ever played were humans. If I'd had a player who wanted to play an alien, I'd have tried to talk him out of it. I wouldn't have forbid it, but I would have argued against it. There's a personal reason for this.
I happen to loathe the Star Blecch/Star Bores presentation of aliens as nothing more than humans in zippered suits or humans with plumbing supplies glued to their foreheads. (Don't even get me started on Star Blecch's various 'crossbreeds'; half-human/half vulcan, etc. Those are right out of D&D and just as silly.) A player playing an alien character is nothing more than someone in a zippered suit.
Aliens should be alien. It should have alien motives, alien feelings, alien thoughts. If not incomprehensible, it should be only barely comprehensible and then in the broadest of brush strokes. Complex interactions on complex subjects between individual humans and individual aliens should be next to impossible, the idea of exchanging religious and philosophical beliefs for example is ludicrous. Face to face communication, even with the aid of computer translation, should be limited, halting, and fraught with error. Trade should be just above the level of barter as ideas and beliefs regarding currency are far too complex a subject.
C.J. Cherryh's Chanur setting is a good example this. While she falls into the trite, silly mold of Star Blecch/Star Bores aliens with the 'Hani' species(1) in those books, she more than redeems the setting with her depictions of the Kif, Stsho, and especially the methane breathing Knnn, Tc'a, and Chi. Those species are actually alien.
The species I've listed in the Chanur setting are about as close to aliens as we're going to get until we meet some. Among Traveller's Major Races, the K'kree and Hivers come closest to matching them as aliens, while the Aslan and Vargr are nothing but zippered suit stereotypes.
In my opinion, you can't realistically or even unrealistically play an alien in a role-playing game without it turning into a satire or stereotype of certain aspects of human behavior. If the group isn't interested in satire, the best that can be done is for the GM to handle an alien as event.
YMMV.
Have fun,
Bill
1 - The Hani might as well just be the Alsan and, seeing as Cherryh's book postdates Traveller, they might very well be the same.