Or is the Swiss view generally more like what it has been historically, that they are neutral and provide a service that others can't.
While initiatives usually fail the popular vote, it is not so certain for this one. It has very broad support. All parties have to argue their position regarding initiatives that will get voted on. So yes certainly there is a debate on such issues.
35 years ago, there was a referendum that would have prevented banking privacy from being used to cover up crime. It failed decisively, but showed that at least 25% of the voters were in favor.
A few years later, after the ouster of Ferdinand Marcos, Swiss banks for the first time in my memory blocked some of his funds, and subsequently the banks were much more circumspect in dealing with dictators.
The next step was the debate about dormant Holocaust era accounts, which led to an official historical commission. That certainly led to domestic debate, which was complicated somewhat by the international pressure under which Switzerland found itself.
And finally, in recent years, after more scandals and stricter banking rules imposed especially by the US, the banks finally seem to be getting out of the organized crime business.
As for "culturally and morally values privacy", I would find that a lot easier to believe if those privacy advocates had equally lobbied for the privacy of salary statements for the employed. But, hey, someone has to keep paying taxes, if the rich don't.
Now, deprived of other unsavory sources of wealth, Swiss Banks are eagerly dabbling in cryptocurrencies.