Fluid layout was the original intent of the Web, after all.
Alas, trusting the browser to broadcast user needs is still a little tricky (and a different question from the subject). Even the default browser font size is still 14px, which is gigantic to most of us. But the default can't change because it will break a bunch of sites that blindly use body { font-size: 85%; }
, users can't well change it for the same reason, and most users don't even know the setting exists.
Most people just want to sit down and browse the Web. Those of us who care about customizing it will find ways to do so, whether by Greasemonkey/Stylish or by clever RSS tricks or by writing our own site that calls some API on yours.
So, to answer both questions: I don't think looking pixel-perfect is all that important, no. They should look roughly the same, I suppose, but I have no problem with e.g. using WebKit and Gecko rounded borders knowing they'll fall back to square corners in Trident and Presto.
Far more important is to just write your site well, so anyone with a drive to customize can do so. Don't rely on what you think the browser defaults are, such as link color or text size; use a CSS reset stylesheet. Use generic fallback for everything, like the serif
font family; not all of us have Arial. Use semantic tags and healthy doses of classes and ids. Don't use Javascript for unnecessary tasks like displaying static content or loading stylesheets. Don't use Flash unless you really have to, and even then provide some open fallback like SVG or <video>
.
I think allowing for user needs relies far more on how flexibly the author makes the site than what a browser does with it.