Firefox does. You have to go enable it in about:config, but it still works fine. Even has per-domain filters so you don't even need the body-id attribute you mentioned. See top example in the README here: https://github.com/NapoleonWils0n/firefox-css
Once upon a time, there was an initiative for websites to add a unique CSS ID to the <body> tag so users could customize them with user stylesheets.
For example: <body id="news-ycombinator-com"> for this website, and then users can apply CSS rules as they see fit via the user stylesheet.
Sadly, the initiative never took off and most browsers nowadays don't even know what a user stylesheet is.