Users see a static HTML view of the forum, so they can read all public posts, but cannot log in to like or reply. (They can still reply via email if that’s configured and they received a notification they can reply to.)
I think you can edit the banner, which you see at the top of the Meta forum in the video Lilly linked, like any text in Discourse (guide). Its key should be js.browser_update.
Unfortunately, your browser is unsupported. Please switch to a supported browser to view rich content, log in and reply.
So adding the link to either the topic on Meta with the suggestions or one of the alternative browsers directly should be possible.
An easy way to see what users see when their browser is outdated is to disable javascript. But I think then you won’t see the banner because the reason isn’t the browser being outdated but javascript being disabled. For that, installing an older browser or using a tool like BrowserStack might be better.