As you can see, people feel strongly about this.
If you tell somebody their browser isn't good enough for your site, you might as well be telling them that their mother is ugly and walks funny.
I realize this (probably) isn't the case with the poster's site, but insisting on a particular brand of browser (typically MSIE) gets the strongest reaction.
I'd guess the next-worst thing you can do is to claim that the user needs a browser "ugrade", when, in fact, they have a newer browser than your site is written for.
There are better ways of handling this than telling the user that their browser isn't up to snuff.
First, try to write your CSS to accommodate the last couple of versions of the most popular browsers. If you are using something extra-special that you really cannot part with, you can detect the browser and serve modified or different style sheets for different browsers.
For older browsers, you can still supply your content in a readable form by serving NO style sheet (for browsers that support style sheets, but just not the version of CSS you are writing to.) There's a bonus to this - if your site is readable, makes sense, and can be navigated with just basic HTML and no style sheet, it will also be reasonably accessible to non-sighted viewers.
You're already detecting the browser, in order to serve the "go away, you're not wanted here" message. Why not just use the same information to omit the style sheet?