Hi Geoff,
Thank you. Your second suggestion helped identify the problem. We are using a membership problem called Magic Members on the site. When deactivated, the community calendar add form is visible, no 502 Bad Gateway error.
Staging site with membership plugin off: http://ebwomen.staging.wpengine.com/member-events/community/add
Thus Magic Members the The Events Calendar Community plugin do not play well together.
However, we need our membership plugin. I plan to share this issue with the developers of the Magic Members plugin, but if you can provide further insight that would be helpful.
Please advise.