I hate it when websites you visit deny you of their service/information if you don't use their desired tools or browser for viewing. It ticks me off to come back to that site whenever I see such warnings. I believe its no longer the trend nowadays. Back when it was still in the early days of web development, it was quite alright to see these warnings, but not anymore.
Webmasters must upgrade their sites to use modern tools.
Upgrade or migration to a later, more modern tool or product is not necessarily a display of riding the bandwagon. Its also to let your users know that you are proactive enough to provide quality and up to date service. Stale use of products or tools would mean that you care less about the service you provide (or at least that's how I see it).
Its already Web 2.0 era, and even more people are inclined to delve into Web 3.0 already, yet a vast majority of the intarweb people are left behind.
Take for example the following sites:
Browsers are intended to be mediums for delivering information!