There isn't a specific idiom that I'm aware of, I'm pretty sure the Economist were just summing up a perceived sentiment with the 'slippery-slope' comment. In Arabic, that sentiment would most likely be expressed in the form of saying that it's laying the groundwork for further cultural drift or something similar, without a particular idiomatic shorthand.

Thing is, even though there's probably phrases like that in regional dialects, they wouldn't be quoted since the majority of Arabic media (and therefore anyone preparing to be quoted by a media outlet) is mostly in Modern Standard Arabic.