With fingerprinting it's not impossible. Quoting a recent Webkit thread[1] in which Google blocked all sign in from non-Safari WebKit browsers:

> But if Google does this properly and uses more sophisticated browser fingerprinting techniques, Epiphany is done for. This could be an existential threat for non-Safari WebKit browsers. Nobody is going to be interested in using a browser that doesn't support Google websites. Google's expressly-stated goal is to block embedded browser frameworks and non-supported browsers from signing into Google accounts. The blog post says: "This block affects CEF-based apps and other non-supported browsers." It says: "We do not allow sign-in from browsers based on frameworks like CEF or Embedded Internet Explorer."

[1] https://lists.webkit.org/pipermail/webkit-dev/2020-November/...

What, you mean like this? (from Chrome)

Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/78.0.3904.108 Safari/537.36

Even if technically impossible, by simply not supporting it - which is already happening - FF will just lose additional market share. I'm at a point where I keep an additional Chromium installed along with my nicely configured FF, because of how many sites doesn't work.