There is a saving grace here, which is that almost nobody who would ship a new grid-based design today is shipping only one layout. They're shipping a family of layouts for different devices.
And once you have a family of layouts, it's not a big deal to add one more layout that covers non-grid-capable browsers.
The design choice that makes this all tenable is to accept that the site isn't supposed to look identical across every browser. You're accepting that you'll do progressive enhancement of layout. Old browsers still get all the content, they will just get it in a more boring format (like all stacked into a single column).
And once you have a family of layouts, it's not a big deal to add one more layout that covers non-grid-capable browsers.
The design choice that makes this all tenable is to accept that the site isn't supposed to look identical across every browser. You're accepting that you'll do progressive enhancement of layout. Old browsers still get all the content, they will just get it in a more boring format (like all stacked into a single column).