If we take the word "possible" to mean "not impossible", then it's still possible. It is however much harder than before.
The circulars from the Central Bank were aimed at shell companies, regardless of where they are incorporated. They do not instruct banks to avoid all non-resident companies.
An effect︀ of this has been a massive reduction in accepted non-resident companies, largely because you can't︁ place your average Seychelles IBC with a Cypriot bank in 99.99% of cases anymore and︂ those constituted a big chunk of the corporate accounts that used to be opened.
In theory, a company can still open a bank in Cyprus if the company has substance︃ in its home country (and as long as that home country is reputable, effectively meaning︄ EU and a handful of other jurisdictions). But many banks in Cyprus will reject it︅ unless it's a very good business case, due to the inherent risks of taking on︆ non-resident companies combined with now also having to ensure that the foreign company has an︇ economic substance there.
The definition of shell company used by the Central Bank is a︈ company with no physical presence or economic activity in its country of incorporation. Notably, though,︉ economic activity can include holding companies (stocks, tangible and intangible assets), companies created for trades/mergers,︊ group companies acting as treasurer, and any other convincing economic activity.