It may seem strange, but some users claim that opening Gmail in an incognito Chrome window is an effective workaround for the Gmail not working in chrome problem. To do that, Launch Google Chrome. Go to the top-right area of the browser, and then click the more icons, which look like three vertically aligned dots. Select New Incognito Window. A new window will show up. Check if the Incognito icon can be seen in the top corner of the window. You can also open an incognito window by pressing Ctrl+Shift+N on your keyboard.
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https://contactforhelp.com/blog/why-my-gmail-wont-load-new-emails-in-chrome-firefox-and-iphone/