Any ad-blocker or otherwise page-modifying Chrome Extension requires the same permissions and likely does the same thing.
Provided the GoLinks extension isn't phoning home with the full contents of the pages its parsing, and immediately discards non-GoLink related data, this shouldn't be a problem.
It would be nice if the GoLinks team could clarify exactly what data is sent back to their servers by the Chrome Extension.
Chrome Extensions can also be inspected and their network traffic can be sniffed quite easily, so independent auditing is possible as well.
Based on what we're hearing from the comments, we're planning to roll out a more detailed privacy page to build more confidence with our users.
I suggest adding an alert anytime a new version of the extension is published, or if you already get an email from Chrome Web Store each time a new extension is published or the email addresses of the Chrome Web Store account are changed (npm does this I believe), to make sure it gets sent to an inbox that's actively monitored.
IMO this permission is something that Chrome should explore, along with other fine-grained permissions. It might be worth making a bug report to Chromium so you can link it when people ask why you ask for such broad permissions. I think the bug report should probably mention that Google uses go links :)
It would still be possible to create a permission that makes it so the code that edits a page can't make any network requests (the output would need to be HTML sanitized, including links), and I'd like to see that, but it would be more difficult to design, implement, and communicate to users.
It's not ideal but in order to make utilities that work on every page, these permissions are needed.
The code inside the extension bundle (.crx) would need to contain the potential for abuse, and if it gets popular enough, security researchers will look at it. Even if it's not popular, incentives will be at work, because it would be a foolish risk for a company to ship code that could expose a user's entire browser history into the extension, because at any point someone could take a look at the bundle and find the flaw.
If you take a look at a company like Grammarly, they've built trust with their users, which is why they can have the "Read and modify all data on all sites" and still have 10 million customers. We plan to build the same trust with our customers.