I'm using Chromium on desktop Linux, I can scroll through recommended content and user profiles without getting the fullscreen login modal anymore. Maybe it's not rolled out to mobile yet?

BTW, I still get this, and it used to just make me go "oh well, I guess they don't want me to look at this web site" and close the window. But someone recently tipped me off to something I am embarrassed I never noticed before: if you actually click "login" on that popup and then cancel the next dialog, you can continue browsing un-pestered.