I really don't understand why you don't want the browser to accept incoming connections, only outgoing ones.
Aren't incoming connections necessary for the browser to function correctly? Can you explain your view in more detail?
Oh, by the way, you could be more careful with phrases like "for sheep", which can be taken in several ways.
In regard to another related aspect, I have found that The Eloston builds of Chromium, available here; (
https://formulae.brew.sh/cask/chromium; click once on the orange-red "eloston-chromium" text, then double click the orange version number after the yellow "Current version:")
will not pop up that annoying message about accepting incoming connections, while other builds
will, despite having the settings in the Security & Privacy preference pane / Firewall settings being set correctly.
I have no proof, but I believe it depends on the build settings, or perhaps even the order of the args or settings used when compiling the binaries.
The Chromium builds available at
https://softaro.net/ungoogled-chromium/ also seem free of that annoying pop up message about allowing incoming connections, and it has the latest version available today, unlike the Eloston site, shown above.
The previous "xattr -csr /Applications/Chromium.app" setting does not work in every case and every Chromium build I have tried (personal experience only), but I don't think it will hurt to try it. See Post #9 above for a link to that prior discussion.