I do use Gmail, and don't have any but have long planned to move to Outlook.com.. perhaps knowing about this ShadowDOM issue will spur me on to make the move.
Google only has one product that's truly best-of-breed (Maps) and I don't mind using it, but don't want to be entirely in any one vendor's ecosystem. I would say Youtube is the best of its kind, but it's really held up by its community, not functionality as Maps is. Outlook may not be the absolute best for privacy either (it's also no-charge), but it at least gets me to a place where I'm well diversified.
Google Maps, Youtube, InoReader, Outlook, DuckDuckGo all on Firefox with containers is a good enough of a spread for me.
If one cannot avoid it, I think it's a better idea to create Chrome desktop shortcuts for Gmail/YouTube and use Chrome exclusively for that, if you cannot use a desktop email client for Gmail and VLC/mpv/youtube-dl for some reason.
Moreover, once you give in on this, what's Google going to do next? Use APIs only in Chrome that Mozilla needs to implement only after they're made public in Chrome by literally looking at the source code? There's always going to be a lag if that's the dynamic, so there's always going to be the perception that Firefox is behind.
Moreover if Firefox adopts it, it makes it more likely to be adopted by Apple too, since Google's now not the only kid on the block to support it and now you turned it into a de-facto standard.
Mozilla already partially caved to Google in pursuit of the "best browser" as perceived by the average user. That was on DRM. Now I say partially because at least they made it opt-in, but so they caved and next Google came up with this thing.
If you going to keep paying ransom, you're going to have a lot of hostages.