Coming back months later to this problem I finally fixed it. You should enter not your store password itself, but Password protection, which you can find in Online store -> preferences -> Password protection.Cheers

After running shopify theme serve command in the terminal and opening http://127.0.0.1:9292 link in the browser, I'm asked to enter the store password, after entering it tells me that the password is incorrect, and I'm sure it is correct. After coupl...