This is not specific to China, but to how chrome/chromium deal with certificates. If you click on the padlock, and then on "certificate information", you should see that the certificate has been issued by godaddy. But this authority is not included by debault in chrome/chromium. You can search on the web how to import godaddy SSL certificate to chrome/chromium (this may depend on your OS), and then it should work fine.
If you suspect a man-in-the-middle attack, you can directly check if the SHA256 fingerprint of the SSL certificate of cloud is
5E 10 38 3B 82 EF E8 E5 05 FE 22 03 17 60 C9 54 68 F1 E1 9C 50 3D 0F B2 69 0F 7D 71 CF E9 82 65
and the SHA1 fingerprint should be
AA 6E 73 4B E1 86 C6 EC E0 61 E9 C3 7E F4 B5 E8 1E 78 BE 9B
(unless someone is also proxying ask.sagemath.org and changing these values on the fly...).
If this is correct, then you should click on "proceed anyway". I am not used to chrome/chromium, but there should be a way to "accept this certificate permanently", and you should do this as well: then, if the certificate changes (e.g. by a man-in-the-middle attack), then you will get a warning.
The problem with storing certificates is that some are stored system-wide, some are stored by the webbrowser, and this depends on the webbrowser and the OS, so i cannot say much more here, and you should read some informations about your configuration.
A possible solution is to try with firefox.
Another possible solution is to install Sage on your computer and use it directly.
Are you saying that you suspect a "man-in-the-middle" from your computer to https://cloud.sagemath.com/ ?