I am pretty sure that ChessCafe is Kaput. These warnings are for your safety when doing online transactions. I would not ignore them.!
Chess Cafe?

The name has been changed; http://chessedu.org/
I got warnings using both Chrome and Firefox just now and I made sure to only try to order things listed as in stock.

When I go to the login page, my Firefox browser says that the connection is untrusted. Also, SSL Labs still reports that the certificate is expired.

yes SSL certificate all fixed.
Agree. SSL Labs now rates the site a mediocre "C" (they use the RC4 cipher suite), but at least the certificate is valid again.
I've recently tried to order some books and software from ChessCafe but my computer says their checkout website is not to be trusted and no one answers their phone? Has anyone bought from them recently and did you just trust their website?