Okay, using the above information I was able to connect Social to FB and Twitter after I contacted Hostgator and had the rule whitelisted. That works.
What isn't working is when a reader tries to click on "Sign in with [Twitter or Facebook]." Rather than sign in, the pop-up window simply displays my home page with this URI:
I'll try talking to HostGator again about this, but has anyone experienced this separate-but-possibly-related issue? If so, was it a different mod_sec rule?