Support the user, not the browser.
It is a fact that most access today is via mobile (source). But you should primarily analyze the audience on your site. The audience is what matters. It’s expected that a site like Stack Overflow, aimed at programmers, will have more desktop access with state-of-the-art browsers. But it’s also expected that a knitting community site will have not so up-to-date browsers. And not only the cliché example of knitting, but there are also companies in which the use of Internet Explorer is mandatory (example).
To measure which browser, operating system, and other metrics your user is using, you can use a tool like the Google Analytics on your website.
From a user experience perspective, there are some options when we talk about old browsers, based on the heuristics of usability:
- Under no circumstances blame the user. The fault of the browser not being supported by your site is yours and not your user’s. He may be using Netscape 8, it’s still your fault.
- Present a usable version of your site without Javascript or CSS. Make sure it’s better than leaving your user with a blank page (as is the case with single-page Applications that fail to load your JS).
- Show a message on the page telling the user that your site looks bad because of the unsupported browser. A message, not a modal, because we don’t want to break the flow.
- If a considerable portion of your access comes from unsupported browsers, add as little CSS and Javascript as is supported by these browsers to improve the experience.