Huh? Which messenger requires a Google account? I've been using both Element and Conversations on Google-free Android devices with accounts not connected to Google for years.
I see how the website gives that impression, which I assume is an attempt to push non-technical users toward an install method that does not lead to support requests and helps fund the project.
The site also mentions that you can build it from source for free, so it's not technically claiming that it's only available from the Play store. If you follow that link, you'll see that availability on F-Droid is prominently displayed on the README.