"Customers not being able to access online banking because the bank stubbornly insists on strong crypto is a far bigger concern than the crypto being broken,"
I also disagree with this.
Some customers would refuse to set a secure password, if given the choice. Convenience trumps security in many cases for many people, no matter how often or vehemently you warn them.
If people are using outdated browsers, redirect them to a page explaining why you must insist that they upgrade, and explain how. This probably doesn't apply to an e-commerce site, but banking is supposed to be secure. If they lead the way, modern standards will be adopted and we will all reap the benefits.