Earlier quoted context omitted.
Aren't both Chrome and Firefox's sync protocols open? At least, the Firefox Sync server is still self-hostable and open source, and at least the client side of Chrome's sync is open source since Chromium can sync as well... I've never understood why someone didn't implement a Firefox Sync extension for Chrome or vice-versa. Is it technical or are people opinionated enough about browsers that no one has the personal n…
For firefox sync on chrome: It’s completely possible, but the crypto is enough of a pain in the ass to deter most people. (It’s also going to be very difficult to implement a robust sync system this way, integration with the underlying storage is all but required for that)
The real problem is data model is significantly different. It's possible, but a lot of boring work, designing the appropriate transformations.