Then you're stuck with Chrome forever. Same with Firefox or Safari. I wish browser vendors would agree on one password sharing protocol that's just some end-to-end encrypted blob that you could download from any browser and unlock with your password. You login to your Firefox or Google account, add passwords, and if you want to use those from the other browser you just get some http link that points to the encrypted blob and then the other browser downloads the blob and you unlock it with a password.
You can export your passwords as a CSV file and import to other browsers (obviously if one chooses to do this, they should delete this file securely after it's been imported).
Firefox, Chrome, and Edge also allow you to import passwords between browsers natively. I'm not saying that I recommend relying on the browser-based password manager (personally I use KeePassX), but I wouldn't advise against it for the reason you're describing. Just sharing some info! Please let me know if I'm mistaken on any of this.
Sure, but if I have a Macbook with Safari and a Linux workstation with Firefox and a Windows gaming PC with Chrome, then I have to use a 3rd party service, right? I don't mind that personally, I'm just an old man yelling "You should have better interoperability between similar competing software services!" at clouds (in the literal and figurative sense).