Final Verdict: W3TC Plugin was rendering cached RSS feeds as text/html, which broke most RSS readers. Disable W3TC until it's patched.
Well, this is annoying, I have scripts that use Simplepie to pull RSS information from our network of Wordpress sites. Unfortunately, this script no longer works since updating to Wordpress 4.3
According to a post in the help forums, W3TC may be the issue. Going to try disabling that now.