Well, it looks like Wells Fargo went ahead and started browser sniffing. I tried to access my account today (like I've been doing every couple of days for the past ... probably 8 years or so), but today, they told me this:

For Online Access with Wells Fargo You Must Use a Supported Browser

Wells Fargo no longer supports the browser version you are using. Please upgrade to a supported browser in order to get access to Wells Fargo's secure sites.

So it's time for me to find another bank. Not just on general principle that I shouldn't be banking with someone who feels the need to tell me what operating system to use, but more because it gives me the impression that their technological staff either doesn't know what they're doing (which I doubt, since they've been good for ~10 years now) or just lost the authority to make their own decisions, and now the monkeys are running things down there. Either way, this is bad, and I don't want my money in it, especially since most of my banking is done online.

So listen up, everybody: don't use Wells Fargo. And I'm shopping around for a new bank, in case you have any recommendations.