There's no mainstream browser that doesn't suck (ie, they're all walled gardens) that supports CSS grid. Plus the other 4 billion people on Earth not in modern countries.
I create my mobile version of pages with Flexbox, so if the user's browser doesn't support it, they see the full featured mobile view. Progressive enhancement.
I build all my mobile layouts with flexbox, so they are usually one long column, and content collapses into the grid from CSS media queries.
If the browser doesn't support css grid, the mobile, single column version with flexbox is fully featured, and is loaded first because the css grid is kept in @media queries.
Like the sibling comment mentioned, you can use @supports, however if you use `display: flex` for mobile and `display: grid` for desktop, the grid will never load in old browsers anyways.
This works out pretty well for me personally in 99% of use cases. If you want to use CSS grid as well for mobile, you'll need a more powerful @supports solution, however.
The walled garden I speak of is the implementation of add-ons cryptographically signed by Mozilla only. Unless you run one of the betas (w/bugs) you cannot use any add-on not approved by Mozilla. And lately they've even been removing/banning add-ons that aren't illegal but otherwise upset outside corporations (ie, the paywall bypasser that uses googlebot's http headers substituted in).
It's important not to lump together the proprietary browsers (where the limit you speak of can only be worked around if the proprietors allow) and free software browsers which respect your software freedom, like Firefox.
You could modify Firefox source code to let you run whatever add-on you wish. With Firefox whatever changes you want are limited only by your willingness to implement them (either by doing the work yourself or working with others to get those changes made).
You can even distribute the improved Firefox variant browser to others and help the community. Hacker News recently had a story about some hackers doing exactly this with a variant they call Librefox. Other examples of Firefox variants include IceCat and the Tor Browser.
Is there a browser you would recommend, if we ignored their HTML/CSS rendering for a second, based on ethical considerations, so to speak? I like making things compatible when I don't need anything modern, and would be interested in hearing about any browsers you think are worth supporting.