I noticed this happening for the past 3 days that when I'm logging into Shopify Admin as well as going to my apps page within admin, I get the unsupported browser error. I even downloaded chrome again thinking it didn't automatically update but that wasn't the problem since I have the latest version. Also because of this error, when I had Captcha enabled within Shopify for my submission pages for the past couple months, these last three days I couldn't log into my store because of Captcha even though the Captcha wouldn't show up..just the same error of having an unsupported browser. Captcha being enabled was fine until the unsupported browser error. Without it, my site gets a lot of spam emails via my contact form.
I'm at a loss why only the past 3 days Chrome isn't considered supported by Shopify even with the latest update..
The exact same thing happened to me! I dont quite know how but i managed to do a chat with a representative and they did nothing about it. They kept telling me to go into Icognito mode which didnt even help anyway. Im having this same exact issue on both Chrome and Firefox. I noticed it on Monday Oct19th. and its still happening.