> Like government websites
I don't know where you live, but as Jake said, government websites are usually the most easy to force into compliance: They (normally) don't have commercial interests, and they (normally) are supposed to cater for the whole population, not just some specific subset thereof.
In short, I don't think that will be a problem. Commercial websites like banks and stuff will, but then I have explicitly told my bank to never ever honor any order made over their web tools. I'm probably special but driving to their nearest branch once a month covers all my banking needs, the rest is cash and credit cards.