The Awakened World is more weird than ours is.
And the shadowrunning world is even moreso.
Yes, a snake as a scarf would be considered pretty weird, and also unprofessional by most Mr Johnsons. But in many places, probably not enough to refuse entry, and many Johnsons are at least somewhat inured to the weird. I mean, there are Nagas, Centaurs, and Pixies doing shadow work, humans who are half-mechanical, and crazy-eyed drug-using Voudoun mages across the table from the Johnson. One more snake-wearing weirdo just means that the group may not be the type to smoothly insert themselves into high society for a fashion heist... but if it has to be done, it's easier to leave the snake at home than for the other weirdos to appear normal.
My opinion as a GM is that anything reasonable that makes characters more interesting, makes the game more interesting and therefore fun for everyone.