While there will be problems with weird characters in SPECIFIC situations, I don't see why it would be a major problem in general.
First, in the world of Shadowrun, the weird walks the streets. Maybe not in a corp enclave, but in a corp enclave it doesn't matter much how weird you are if you're even slightly weird, so the cybered-up street sam is going to have the same problems as the centaur.
Second, there are many characters whose appearance is irrelevant. Riggers, deckers, and summons/buff mages quite often don't have to deal with either clients or targets, and often not even with bystanders. So you can make a weird character work by making them one of these "behind the scenes" characters.
Third, there is Physical Mask, Disguise, and several disguise-oriented Adept powers.
Fourth, and going back to second... there is a large group of "intermediate interaction" characters who don't necessarily hide out of the active area, but who also don't necessarily meet and greet NPCs. That street sam from the first point, especially if he's Uncouth or trigger-happy? Why would you want him to get too involved, until it becomes time to actually get "involved", and by that I mean to come in shooting? If you have a frog changeling, he shouldn't be meeting with NPCs until it comes time to either sneak around (and if you're discovered, then your appearance is probably a lot less important than the fact that you shouldn't be there), or shoot (at which point what matters is the caliber of your weapon rather than how many tentacles you have). So there are a lot of characters, both weird and normal in appearance, who may interact with NPCs mostly in situations where appearance is not very relevant.
So, unless you want to play a character who is both weird and a Face, or an infiltrator, or some other kind of character who regularly deals with NPCs in peaceful/social interactions, it should not be a major problem. Yeah, if you're a frog changeling, you're probably not spending your free time going to the opera, or to an Urban Brawl game, or to a nice restaurant. So get used to playing Matrix Games and watching sims for entertainment as if you were some anti-social character like a Decker. But having your character's entertainment options limited is far from the kind of issue that makes characters really difficult to play.
A Naga? That's difficult. A frog changeling? That's merely different.