When trying to access a couple of high-profile websites (*.apple.com, twitter.com) via HTTPS, they've since recently been getting their certificates rejected by some client apps (Chrome, App Store, curl) but not by others (Safari, Firefox, wget, lynx).
This is a bit paralyzing, because with App Store unable to talk to identity.apple.com I can't get OS updates anymore.
I'm running OSX 10.9.5 on a 2013 rMBP. I'm not aware of having made any major changes in the system recently. Not using any network-sniffing or otherwise unusual software. I haven't been messing with stored certificate-authority data - I wouldn't even quite know how to do that. I do have Homebrew-installed OpenSSL, if that changes anything.
Could anyone help me fix this?