It's reasonable to withdraw support for old browsers. It's not reasonable to completely block users from using the site. (This used to be a thing I found extremely irksome in the 90s when using Opera or another perfectly capable browser that the web designer wasn't fluent in.) I understand that there is a desire to preserve a certain amount of control over the user experience to ensure your vision is true, but blocking access is not the solution. Some people don't have the luxury of upgrading the browser they use in all contexts (be it work, a public terminal, a paranoid family member's computer, etc.), so the directive to upgrade without an option to bypass is just plain frustrating. Any compromise (such as requiring a click-through every time with a persistent banner) is better than not being able to access the site at all. Let an informed user be the final judge over whether they're willing to access the site with a substandard browser.